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Slow Invariant Manifolds of Memristor-Based Chaotic Circuits Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-12 Jean-Marc Ginoux, Riccardo Meucci, Guanrong Chen, Leon O. Chua
This work presents an efficient approach for computing the slow invariant manifold of the fourth-order canonical memristor-based Chua circuits using the flow curvature method. First, the magnetic-flux and charge characteristic curve is generated from the classical circuit with a piecewise-linear function. Then, the characteristic curve is generated from the circuit with the piecewise-linear function
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3D Generating Surfaces in Hamiltonian Systems with Three Degrees of Freedom – I Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-12 Matthaios Katsanikas, Stephen Wiggins
In our earlier research (see [Katsanikas & Wiggins, 2021a, 2021b, 2023a, 2023b, 2023c]), we developed two methods for creating dividing surfaces, either based on periodic orbits or two-dimensional generating surfaces. These methods were specifically designed for Hamiltonian systems with three or more degrees of freedom. Our prior work extended these dividing surfaces to more complex structures such
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3D Generating Surfaces in Hamiltonian Systems with Three Degrees of Freedom – II Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-12 Matthaios Katsanikas, Stephen Wiggins
Our paper is a continuation of a previous work referenced as [Katsanikas & Wiggins, 2024b]. In this new paper, we present a second method for computing three-dimensional generating surfaces in Hamiltonian systems with three degrees of freedom. These 3D generating surfaces are distinct from the Normally Hyperbolic Invariant Manifold (NHIM) and have the unique property of producing dividing surfaces
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Dynamic Complexities in Competing Parasitoid Species on a Shared Host Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-12 Lijiao Jia, Yunil Roh, Guangri Piao, Il Hyo Jung
In this study, we extend the two-dimensional host–parasitoid model to a one-host–two-parasitoid model, whose dynamic behaviors are more complex. As evidence, exploring the dynamic interaction between a host and its parasitoids provides significant insight into the biological control. Specifically, we demonstrate the existence of equilibrium points and explore their local stability properties, which
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Bistability and Bifurcations of Tumor Dynamics with Immune Escape and the Chimeric Antigen Receptor T-Cell Therapy Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-12 Shaoli Wang, Tengfei Wang, Xiyan Bai, Shaoping Ji, Tianhai Tian
Tumor immune escape refers to the inability of the immune system to clear tumor cells, which is one of the major obstacles in designing effective treatment schemes for cancer diseases. Although clinical studies have led to promising treatment outcomes, it is imperative to design theoretical models to investigate the long-term treatment effects. In this paper, we develop a mathematical model to study
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Weak Sensitive Compactness for Linear Operators Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-12 Quanquan Yao, Peiyong Zhu
Let (X,T) be a linear dynamical system, where X is a separable Banach space and T:X→X is a bounded linear operator. We show that if (X,T) is invertible, then (X,T) is weakly sensitive compact if and only if (X,T) is thickly weakly sensitive compact; and that there exists a system (X×Y,T×S) such that: (1) (X×Y,T×S) is cofinitely weakly sensitive compact; (2) (X,T) and (Y,S) are weakly sensitive compact;
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Emergence of Hidden Strange Nonchaotic Attractors in a Rational Memristive Map Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-12 Premraj Durairaj, Sathiyadevi Kanagaraj, Zhigang Zheng, Anitha Karthikeyan, Karthikeyan Rajagopal
To exemplify the existence of hidden strange nonchaotic attractors (HSNAs) and transition mechanism, we consider a rational memristive map with additional force. We find that the four-torus bifurcates into the eight-torus through torus doubling as a function of the control parameter. Following that, the formation of strange nonchaotic attractors occurs when increasing the control parameter. As a result
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Dynamic Relationship Between Informal Sector and Unemployment: A Mathematical Model Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-12 A. K. Misra, Mamta Kumari
Shortage of formal jobs, lack of skills in workforce and increasing human population proliferate the informal sector. This sector provides an opportunity to unskilled workers to gain skills along with earnings. In this paper, a deterministic nonlinear mathematical model is developed to study the effects of informal skill learning and job generation on unemployment. For the formulated system, feasibility
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Impact of Fear and Group Defense on the Dynamics of a Predator–Prey System Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-12 Soumitra Pal, Sarbari Karmakar, Saheb Pal, Nikhil Pal, A. K. Misra, Joydev Chattopadhyay
To reduce the chance of predation, many prey species adopt group defense mechanisms. While it is commonly believed that such defense mechanisms lead to positive feedback on prey density, a closer observation reveals that it may impact the growth rate of species. This is because individuals invest more time and effort in defense rather than reproductive activities. In this study, we delve into a predator–prey
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Bifurcation Analysis of a Discrete Amensalism Model Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-12 Xinli Hu, Hanghang Li, Fengde Chen
By using model discretization of the piecewise constant argument method, a discrete amensalism model with nonselective harvesting and Allee effect is formulated. The dynamic analysis of the model is studied and the existence and stability of the equilibrium point are discussed. The fold bifurcation and flip bifurcation at the equilibrium point of the system are proved by using the bifurcation theory
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Bifurcation Analysis of a Predator–Prey Model with Alternative Prey and Prey Refuges Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-12 Wenzhe Cui, Yulin Zhao
In this paper, we study the codimensions of Hopf bifurcation and Bogdanov–Takens bifurcation of a predator–prey model with alternative prey and prey refuges, which was proposed by Chen et al. [2023]. The results show that the predator–prey model can undergo a supercritical Hopf bifurcation or a Bogdanov–Takens bifurcation of codimension two under certain parameter conditions. It means that there are
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Coupled HR–HNN Neuron with a Locally Active Memristor Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-12 Lili Huang, Shaotian Wang, Tengfei Lei, Keyu Huang, Chunbiao Li
Local activity could be the source for complexity. In this study, a multistable locally active memristor is proposed, whose nonvolatile memory, as well as locally active characteristics, is validated by the power-off plot and DC V–I plot. Based on the two-dimensional Hindmarsh–Rose neuron and a one-dimensional Hopfield neuron, a simple neural network is constructed by connecting the two neurons with
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Optimal and Poor Synchronizations of Directionally Coupled Phase-Coherent Chaotic Oscillators Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-12 Yong Lei, Xin-Jian Xu, Xiaofan Wang
We study directionally coupled phase-coherent chaotic oscillators in complex networks. We introduce an adjusted Lyapunov function that incorporates the frequencies of the oscillators and the interaction structure. Using the well-known Rössler system as an example, we address two optimization problems: frequency allocation and network design. Through numerical experiments, we demonstrate that the systematic
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Stabilization of Laminars in Chaos Intermittency Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-12 Michiru Katayama, Kenji Ikeda, Tetsushi Ueta
Chaos intermittency is composed of a laminar regime, which exhibits almost periodic motion, and a burst regime, which exhibits chaotic motion; it is known that in chaos intermittency, switching between these regimes occurs irregularly. In the laminar regime of chaos intermittency, the periodic solution before the saddle node bifurcation is closely related to its generation, and its behavior becomes
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Stability, Bifurcation and Dynamics in a Network with Delays Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-12 Xu Xu, Jianming Liu
In real-world networks, due to complex topological structures and uncertainties such as time delays, uncontrolled systems may generate instability and complexity, thereby degrading network performance. This paper provides a detailed analysis of the stability, Hopf bifurcation, and complex dynamics of a networked system under delayed feedback control. Based on the linear stability method and Hopf bifurcation
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From 1D Endomorphism to Multidimensional Hénon Map: Persistence of Bifurcation Structure Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-12 V. N. Belykh, N. V. Barabash, D. A. Grechko
The renowned 2D invertible Hénon map turns into 1D noninvertible quadratic map when its leading parameter b becomes zero. This well-known link was studied by Mira who demonstrated that the bifurcation set of Hénon diffeomorphism is similar to his “box-within-a-box” bifurcation structure of 1D endomorphism. In general, such similarity has not been strictly established, especially in multidimensional
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Study of Short-Term and Long-Term Memories by Hodgkin–Huxley Memristor Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-12 L. Wen, C. K. Ong
Long-term memory (LTM ) and short-term memory (STM ) and their evolution from one to the other are important mechanisms to understand brain memory. We use the Hodgkin–Huxley (HH ) model, a well-tested and closest model to biological neurons and synapses, to shine some light on LTM and STM memorization mechanisms. The role of Na+ and K+ion channels playing in LTM and STM process is carefully examined
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On–Off Intermittency and Long-Term Reactivity in a Host–Parasitoid Model with a Deterministic Driver Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-12 Fasma Diele, Deborah Lacitignola, Angela Monti
Bursting behaviors, driven by environmental variability, can substantially influence ecosystem services and functions and have the potential to cause abrupt population breakouts in host–parasitoid systems. We explore the impact of environment on the host–parasitoid interaction by investigating separately the effect of grazing-dependent habitat variation on the host density and the effect of environmental
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Transition and Propagation of Epilepsy in an Improved Epileptor Model Coupled with Astrocyte Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-11 Kangning An, Lin Du, Honghui Zhang, Zhuan Shen, Xiaojuan Sun
In this paper, a tripartite synapse network is constructed to examine external and internal triggering factors of epilepsy transition and propagation in neurons with the Epileptor-2 model. We first explore the external stimuli in the environment that induce epileptic activities and transition behaviors among Ictal Discharges (IDs) and Interictal Discharges (IIDs) states. The higher the strength and
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Dynamic Analysis of a Ratio-Dependent Food Chain Model with Prey-Taxis Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-09 Zhuzhen Liao, Cui Song, Zhi-Cheng Wang
In this paper, we consider a food chain model with ratio-dependent functional response and prey-taxis. We first investigate the global existence and boundedness of the unique positive classical solutions of the system in a bounded domain with smooth boundary and Neumann boundary conditions. Then, we analyze the local stability of the system and the existence of Hopf bifurcation. In addition, we prove
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A Lightweight CNN Based on Memristive Stochastic Computing for Electronic Nose Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-06 Bin Yang, Tao Chen, Ai Chen, Shukai Duan, Lidan Wang
Gas detection plays different roles in different environments. Traditional algorithms implemented on electronic nose for gas detection and recognition have high complexity and cannot resist device drift. In response to the above issues, we propose a convolutional neural network based on memristive Stochastic Computing (SC), which combines the characteristics of small devices and low power consumption
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Stability Analysis and Simulation of a Delayed Dengue Transmission Model with Logistic Growth and Nonlinear Incidence Rate Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-06 Fangkai Guo, Xiaohong Tian
In this work, a dengue transmission model with logistic growth and time delay (τ) is investigated. Through detailed mathematical analysis, the local stability of a disease-free equilibrium and an endemic equilibrium is discussed, the existence of Hopf bifurcation and stability switch is established, and it is proved that the system is permanent if the basic reproduction number is greater than 1. On
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Four Limit Cycles of Three-Dimensional Discontinuous Piecewise Differential Systems Having a Sphere as Switching Manifold Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-06 Louiza Baymout, Rebiha Benterki
Because of their applications, the study of piecewise-linear differential systems has become increasingly important in recent years. This type of system already exists to model many different natural phenomena in physics, biology, economics, etc. As is well known, the study of the qualitative theory of piecewise differential systems focuses mainly on limit cycles. Most papers studying the problem of
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Dynamics of a Class of Prey–Predator Models with Singular Perturbation and Distributed Delay Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-06 Jie Gao, Yue Zhang
In this paper, two prey–predator models with distributed delays are presented based on the growth and loss rates of the predator, which are much smaller than that of the prey, leading to a singular perturbation problem. It is obtained that Hopf bifurcation can occur, where the coexistence equilibrium becomes unstable leading to a stable limit cycle. Subsequently, considering the perturbation parameter
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Global Phase Portraits of Piecewise Quadratic Differential Systems with a Pseudo-Center Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-06 Meriem Barkat, Rebiha Benterki, Enrique Ponce
This paper deals with the global dynamics of planar piecewise smooth differential systems constituted by two different vector fields separated by one straight line that passes through the origin. From a quasi-canonical family of piecewise quadratic differential systems with a pseudo-focus point at the origin, which has six parameters, we investigate the subfamilies where the origin is indeed a pseudo-center
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Geometrical and Numerical Analysis of Predator–Prey System Based on the Allee Effect in Predator Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-06 M. K. Gupta, Abha Sahu, C. K. Yadav
This study explores the complex dynamics of the predator–prey interactions, with a specific emphasis on the influence of the Allee effect on the predator population. We examined the fundamental mathematical characteristics of the model under consideration, such as the positivity of the system and the boundedness of the solutions. We investigated the equilibrium points and analyzed their stability using
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Finite-Time Synchronization of Fractional-Order Nonlinear Systems with State-Dependent Delayed Impulse Control Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-06 P. Gokul, S. S. Mohanrasu, A. Kashkynbayev, R. Rakkiyappan
This paper delves into the topics of Finite-Time Stabilization (FTS) and Finite-Time Contractive Stabilization (FTCS) for Fractional-Order Nonlinear Systems (FONSs). To address these issues, we employ a State-Dependent Delayed Impulsive Controller (SDDIC). By leveraging both Lyapunov theory and impulsive control theory, we establish sufficient conditions for achieving stability criteria for fractional-order
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Bifurcations of Sliding Heteroclinic Cycles in Three-Dimensional Filippov Systems Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-06 Yousu Huang, Qigui Yang
Global bifurcations with sliding have rarely been studied in three-dimensional piecewise smooth systems. In this paper, codimension-2 bifurcations of nondegenerate sliding heteroclinic cycle Γ are investigated in three-dimensional Filippov systems. Two cases of sliding heteroclinic cycle are discussed: (C1) connecting two saddle-foci, (C2) connecting one saddle-focus and one saddle. It is proved that
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Existence and Uniqueness of a Canard Cycle with Cyclicity at Most Two in a Singularly Perturbed Leslie–Gower Predator–Prey Model with Prey Harvesting Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-06 Zhenshu Wen, Tianyu Shi
Yao and Huzak [2022] proved that the cyclicity of canard cycles in a singularly perturbed Leslie–Gower predator–prey model with prey harvesting is at most two in a region of parameters. In this paper, we further show that there exists only one canard cycle with cyclicity at most two under explicit parameters conditions.
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The Effects of Negative Regulation on the Dynamical Transition in Epileptic Network Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-06 Songan Hou, Haodong Wang, Denggui Fan, Ying Yu, Qingyun Wang
The transiting mechanism of abnormal brain functional activities, such as the epileptic seizures, has not been fully elucidated. In this study, we employ a probabilistic neural network model to investigate the impact of negative regulation, including negative connections and negative inputs, on the dynamical transition behavior of network dynamics. It is observed that negative connections significantly
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Bifurcations and Exact Solutions of a Cantilever Beam Vibration Model Without Damping and Forced Terms Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-06 Jinsen Zhuang, Guanrong Chen, Jibin Li
For the cantilever beam vibration model without damping and forced terms, the corresponding differential system is a planar dynamical system with some singular straight lines. In this paper, by using the techniques from dynamical systems and singular traveling wave theory developed by [Li & Chen, 2007] to analyze its corresponding differential system, the bifurcations and the dynamical behaviors of
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Memory Maps with Elliptical Trajectories Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2023-08-05 Ted Szylowiec, Paweł Góra
A family of maps with memory, parameterized by α, is shown to have either periodic trajectories or dense trajectories on ellipses which support absolutely continuous invariant measures. Furthermore, for 0<α<12, i.e. α=2cos𝜃2cos𝜃−1 with 𝜃=r(2π) and 14
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Basin Entropy and Wada Property of Magnetic Field Line Escape in Toroidal Plasmas with Reversed Shear Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2023-08-05 P. Haerter, L. C. de Souza, A. C. Mathias, R. L. Viana, I. L. Caldas
The structure of magnetic field lines in toroidal fusion plasmas, as in tokamaks and stellarators, represents the lowest-order description of the plasma particle behavior, up to finite Larmor and drift effects. Tokamaks with reversed magnetic shear typically present internal transport barriers that help to improve confinement through a partial or total reduction of the particle transport across magnetic
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Pure-Attention-Based Multifunction Memristive Neuromorphic Circuit and System Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2023-08-05 He Xiao, Haohang Sun, Tianhao Zhao, Yue Zhou, Xiaofang Hu
The use of memristive neuromorphic circuit and system is a promising solution for next-generation Artificial Intelligence (AI) computing, as it offers possibilities that go beyond conventional GPU-based artificial neural network computing platforms. However, most of the existing memristive neuromorphic circuits and systems are designed for the specific networks, which is lack of universality and flexibility
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Bifurcation Analysis and Steady-State Patterns in Reaction–Diffusion Systems Augmented with Self- and Cross-Diffusion Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2023-08-05 Benjamin Aymard
In this article, a study of long-term behavior of reaction–diffusion systems augmented with self- and cross-diffusion is reported, using an augmented Gray–Scott system as a generic example. The methodology remains general, and is therefore applicable to some other systems. Simulations of the temporal model (nonlinear parabolic system) reveal the presence of steady states, often associated with energy
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Switching Signals Design for Generating Chaos from Two Linear Systems Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2023-08-05 Changchun Sun
A problem on how to generate chaos from two 3D linear systems via switching control is investigated. Each linear system has the simplest algebraic structure with three parameters. Two basic conditions of all parameters are given. One of two linear systems is stable. The other is unstable. Switching signals of different quadratic surfaces are designed respectively to generate chaotic dynamical behaviors
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Rayleigh–Bénard Convection of Water-Copper and Water-Alumina Nanofluids Based on Minimal- and Higher-Mode Lorenz Models Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2023-08-05 P. G. Siddheshwar, Ruwaidiah Idris, C. Kanchana, D. Laroze
Linear and nonlinear stability analyses of Rayleigh–Bénard convection in water-copper and water-alumina nanofluids are studied in the paper by considering a minimal as well as an extended truncated Fourier representation. These representations respectively result in a third-order classical Lorenz model and a five-dimensional extended Lorenz model. The marginal stability plots reveal that the influence
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Nonlinear Vibration Analysis of the Coupled Gear-Rotor-Bearing Transmission System for a New Energy Vehicle Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2023-08-05 Shuai Mo, Zhen Wang, Yanjun Zeng, Wei Zhang
Considering the effects of time-varying meshing stiffness, time-varying support stiffness, transmission errors, tooth side clearance and bearing clearance, a nonlinear dynamics model of the coupled gear-rotor-bearing transmission system of a new energy vehicle is constructed. Firstly, the fourth-order Runge–Kutta integral method is used to solve the differential equations of the system dynamics, and
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Hopf Bifurcation Analysis of a Housefly Model with Time Delay Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2023-08-05 Xiaoyuan Chang, Xu Gao, Jimin Zhang
The oscillatory dynamics of a delayed housefly model is analyzed in this paper. The local and global stabilities at the non-negative equilibria are obtained via analyzing the distribution of eigenvalues and Lyapunov–LaSalle invariance principle, and the model undergoes the supercritical Hopf bifurcation and the transient oscillation. Based on Wu’s global Hopf bifurcation theory, the existence of the
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The Boundedness Locus and Baby Mandelbrot Sets for Some Generalized McMullen Maps Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2023-08-05 Suzanne Boyd, Alexander J. Mitchell
In this paper, we study rational functions of the form Rn,a,c(z)=zn+azn+c, with n fixed and at least 3, and hold either a or c fixed while the other varies. We locate some homeomorphic copies of the Mandelbrot set in the c-parameter plane for certain ranges of a, as well as in the a-plane for some c-ranges. We use techniques first introduced by Douady and Hubbard [1985] that were applied for the subfamily
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Solution Structures of an Electrical Transmission Line Model with Bifurcation and Chaos in Hamiltonian Dynamics Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2023-08-05 Jianming Qi, Qinghua Cui, Le Zhang, Yiqun Sun
Employing the Riccati–Bernoulli sub-ODE method (RBSM) and improved Weierstrass elliptic function method, we handle the proposed (2+1)-dimensional nonlinear fractional electrical transmission line equation (NFETLE) system in this paper. An infinite sequence of solutions and Weierstrass elliptic function solutions may be obtained through solving the NFETLE. These new exact and solitary wave solutions
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Uncovering the Correlation Between Spindle and Ripple Dynamics and Synaptic Connections in a Hippocampal-Thalamic-Cortical Model Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2023-08-05 Sridevi Sriram, Hayder Natiq, Karthikeyan Rajagopal, Fatemeh Parastesh, Sajad Jafari
Consolidation of new information in memory occurs through the simultaneous occurrence of sharp-wave ripples (SWR) in the hippocampus network, fast–slow spindles in the thalamus network, and up and down oscillations in the cortex network during sleep. Previous studies have investigated the influential and active role of spindles and sharp-wave ripples in memory consolidation. However, a detailed investigation
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Fixed-/Preassigned-Time Stability Control of Chaotic Power Systems Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2023-08-05 Leimin Wang, Yu Zhou, Da Xu, Qiang Lai
A power system shows chaotic oscillation when it is subjected to periodic load disturbance, which makes it a challenging and interesting problem for stability control of chaotic power system. In this paper, a unified controller is designed to solve the fixed-time and preassigned-time stability problems of fourth-order chaotic power systems. In addition, based on Lyapunov stability theory, sufficient
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Homoclinic Bifurcations in a Class of Three-Dimensional Symmetric Piecewise Affine Systems Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2023-08-05 Ruimin Liu, Minghao Liu, Tiantian Wu
Many physical and engineering systems have certain symmetric properties. Homoclinic orbits play an important role in studying the global dynamics of dynamical systems. This paper focuses on the existence and bifurcations of homoclinic orbits to a saddle in a class of three-dimensional one-parameter three-zone symmetric piecewise affine systems. Based on the analysis of the Poincaré maps, the systems
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Stochastic Bifurcations and Multistage Order–Chaos Transitions in a 4D Eco-Epidemiological Model Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2023-08-05 Lev Ryashko, Tatyana Perevalova, Irina Bashkirtseva
A tritrophic “prey-intermediate predator-top predator” population system with disease in the intermediate predator is considered. For this 4D-model, the bifurcation analysis is performed. In this analysis, the rate of the disease transmission is used as a bifurcation parameter. A variety of mono-, bi- and tri-stable behaviors with regular and chaotic attractors are analyzed. It is shown how random
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Parametric Topological Entropy for Multivalued Maps and Differential Inclusions with Nonautonomous Impulses Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2023-08-05 Jan Andres, Pavel Ludvík
The main purpose of this paper is to investigate a parametric topological entropy for impulsive differential inclusions on tori. In this way, besides other matters, we would like to extend our recent results concerning impulsive differential equations as well as those on “nonparametric” topological entropy to impulsive differential inclusions. Parametric topological entropy, which is usually called
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A Synopsis of the Noninvertible, Two-Dimensional, Border-Collision Normal Form with Applications to Power Converters Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2023-07-03 Hammed Olawale Fatoyinbo, David J. W. Simpson
The border-collision normal form is a canonical form for two-dimensional, continuous maps comprised of two affine pieces. In this paper, we provide a guide to the dynamics of this family of maps in the noninvertible case where the two pieces fold onto the same half-plane. Most significantly we identify parameter regimes for the occurrence of key bifurcation structures, such as period-incrementing,
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The Generalization of the Periodic Orbit Dividing Surface for Hamiltonian Systems with Three or More Degrees of Freedom – IV Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2023-07-03 Matthaios Katsanikas, Stephen Wiggins
Recently, we presented two methods of constructing periodic orbit dividing surfaces for Hamiltonian systems with three or more degrees of freedom [Katsanikas & Wiggins, 2021a, 2021b]. These methods were illustrated with an application to a quadratic normal form Hamiltonian system with three degrees of freedom. More precisely, in these papers we constructed a section of the dividing surfaces that intersect
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A Novel Chaotic Image Encryption Algorithm Based on Propositional Logic Coding Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2023-07-03 Haiping Chang, Erfu Wang, Jia Liu
This paper proposes a new chaotic system 2D-HLM, which is a combination of Henon map and logistic map. SHA-256 algorithm based on the plaintext image produces the initial value, which enhances the correlation with the plaintext. Therefore, the algorithm avoids the disadvantages of being easily cracked by selected plaintext attacks. The chaotic sequence generated by 2D-HLM is adopted to scramble an
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Dynamics and Circuit Implementation of a 4D Memristive Chaotic System with Extreme Multistability Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2023-07-03 Shaohui Yan, Yu Ren, Binxian Gu, Qiyu Wang, Ertong Wang
In this paper, a four-dimensional chaotic system based on a flux-controlled memristor with cosine function is constructed. It has infinitely many equilibria. By changing the initial values x(0), z(0) and u(0) of the system and keeping the parameters constant, we obtained the distribution of infinitely many single-wing and double-wing attractors along the u-coordinate, which verifies the initial-offset
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Bifurcation Behavior Analysis and Stability Region Discrimination for Series-Parallel Architecture Electric Energy Router Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2023-07-03 Xiaojun Zhao, Zehui Zhang, Chunjiang Zhang, Xiaohuan Wang, Zhongnan Guo
Electric energy routers (EERs) can effectively deal with the energy management issues caused by the access of multi-sources and multi-loads. Different from the energy transmission form in the existing series architecture EER (SA-EER) for low-voltage distribution networks, a new series-parallel architecture EER (SPA-EER) has the advantages of high-power transmission capability and reactive power flexible
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Scaling Analysis at Transition of Chaos Driven by Euler’s Numerical Algorithm Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2023-07-03 Jinde Cao, Ashish
Chaos is a nonlinear phenomenon that reveals itself everywhere in nature and in many fields of science. It has gained increasing attention from researchers and scientists over the last two decades. In this article, the nature of the fixed and periodic states are examined for a discrete two-parameter map; a composition of Euler’s numerical map and the logistic map. Further, the dynamical properties
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Slow–Fast Dynamics of a Coupled Oscillator with Periodic Excitation Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2023-07-03 Yibo Xia, Jingwei He, Jürgen Kurths, Qinsheng Bi
We study the influence of the coexisting steady states in high-dimensional systems on the dynamical evolution of the vector field when a slow-varying periodic excitation is introduced. The model under consideration is a coupled system of Bonhöffer–van der Pol (BVP) equations with a slow-varying periodic excitation. We apply the modified slow–fast analysis method to perform a detailed study on all the
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2D Linear CA with Mixing Boundary Conditions and Reversibility Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2023-07-03 Doston Jumaniyozov, José Manuel Casas, Manuel Ladra González, Bakhrom Omirov, Shovkat Redjepov
In this paper, we consider two-dimensional cellular automata (CA) with the von Neumann neighborhood. We study the characterization of 2D linear cellular automata defined by the von Neumann neighborhood with new type of boundary conditions over the field ℤp. Furthermore, we investigate the rule matrices of 2D von Neumann CA by applying the group of permutations S4. Moreover, the algorithm for computing
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Managing the Use of Insecticides in Agricultural Fields: A Modeling Study Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2023-07-03 A. K. Misra, Akash Yadav
At present time, sustainable crop production is of prime importance due to the expansion of human population and diminishing cultivable land. Insects attack the plants’ roots, blooms and leaves and lessen the agricultural production across the globe. In this research work, we propose a nonlinear mathematical model to manage the spray of insecticides to control insect population and increase crop production
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A Robust Chaotic Map and Its Application to Speech Encryption in Dual Frequency Domain Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2023-07-03 Yi-Bo Huang, Peng-Wei Xie, Jun-Bin Gao, Qiu-Yu Zhang
When chaotic systems are used for speech encryption, their chaotic performance largely determines the security of speech encryption. However, traditional chaotic systems have problems such as parameter discontinuity, easy occurrence of chaos degradation, low complexity, and the existence of periodic windows in chaotic intervals. In real applications, chaotic mappings may fall into periodic windows
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Chaos and Bistabilities in a Food-Chain Model with Allee Effect and Additional Food Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2023-07-03 Nikhilesh Sil, Sudip Samanta
In this research article, a three-species food chain model with Allee effect and additional food is proposed and analyzed. The Allee effect and additional food are introduced to the top predator population. The dynamical behavior of the system is studied analytically and numerically. We have performed equilibrium analysis and local stability analysis around the non-negative equilibria. We have also
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Global Dynamics of a Predator–Prey Model with Simplified Holling Type IV Functional Response and Fear Effect Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2023-07-03 Jianglong Xiao, Yonghui Xia
In this paper, we study one type of predator–prey model with simplified Holling type IV functional response by incorporating the fear effect into prey species. The existence and stability of all equilibria of the system are studied. And bifurcation behaviors including saddle-node bifurcation, transcritical bifurcation and Hopf bifurcation of the system are completely explored. Numerical simulation
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Chaotic Behaviors of a Delay Partial Difference Equation with a Delay Controller Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2023-07-03 Yongjun Zhang, Wei Liang, Xuanxuan Zhang
A delay partial difference equation with a delay controller is studied in this paper. We show that it can lead to both Devaney chaos and Li–Yorke chaos by applying the modified Marotto’s theorem, with three criteria established for generating chaos. Computer simulations of chaotic behaviors and spatiotemporal graphs are performed with three examples.
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Blow-Up Method for Linearizability of Resonant Differential Systems Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2023-07-03 Brigita Ferčec, Maja Žulj, Jaume Giné
In this paper, the linearizability of a p:−q resonant differential system is studied. First, we describe a method to compute the necessary conditions for linearizability based on blow-up transformation. Using the method, we compute necessary linearizability conditions for a family of 1:−3 resonant system with quadratic nonlinearities. The sufficiency of the obtained conditions is proven either by the