Threshold policy is more realistic than continuous control for biological system management. Most related works are devoted to studying a single-threshold value for one single population, thereby avoiding complicated mathematical analysis of the nonsmooth differential equations. Based on the fact that numerical simulations play an important role in analyzing and understanding the intrinsic mechanism

This paper presents a global study of the class QsnSN11 of all real quadratic polynomial differential systems which have a finite semi-elemental saddle-node and an infinite saddle-node formed by the coalescence of a finite singularity and an infinite singularity. This class can be divided into two different families, namely, QsnSN11(A) phase portraits possessing a finite saddle-node as the only finite

Giving customers queue length information about a service system has the potential to influence the decision of a customer to join a queue. Thus, it is imperative for managers of queueing systems to understand how the information that they provide will affect the performance of the system. To this end, we construct and analyze a two-dimensional deterministic fluid model that incorporates customer choice

As image is an important way of information representation, researchers pay more and more attention on image encryption. In order to improve the performance of image encryption, a novel image encryption scheme based on a hybrid cascaded chaotic system and sectoral segmentation is proposed in this paper. Hybrid cascaded chaotic system has a larger key space, higher complexity, more sensitivity to initial

In this work, several new aspects of the dynamics of the well-known TNC hyperchaotic oscillator are investigated. Numerous novelties appear in this work, namely particular structures of space magnetization, the coexistence of bursting patterns, the coexistence of up to four asymmetric different attractors, offset-boosting, and antimonotonicity. In addition to this interesting and particular combination

The effect of retardation along second vector of angular velocity on a new attitude system of quad-rotor unmanned aerial vehicle (QUAV) is examined in this paper. Catastrophic and hovering conditions of rotor dynamics are verified through bifurcation analysis. It is analyzed that disturbed rotor dynamics during yaw maneuvering lead towards the existence of oscillations and hamper the efficiency of

In this paper, we study Poincaré bifurcation of a class of piecewise polynomial systems, whose unperturbed system has a period annulus together with two invariant lines. The main concerns are the number of zeros of the first order Melnikov function and the estimation of the number of limit cycles which bifurcate from the period annulus under piecewise polynomial perturbations of degree n.

Complexity is an important feature of complex time series. In this paper, we construct a weighted dispersion pattern and propose a new entropy plane using past Tsallis entropy and past Rényi entropy by using weighted dispersion pattern (PTEWD and PREWD, respectively), to quantify the complexity of time series. Through analyzing simulated data and actual data, we have verified the reliability of the

By using center manifold theory, Poincaré–Bendixson theorem, spatiotemporal spectrum and dispersion relation of linear operators, the spatiotemporal dynamics of an activator-substrate model with double saturation terms under the homogeneous Neumann boundary condition are considered in the present paper. It is surprising to find that the system can induce new dynamics, such as subcritical Hopf bifurcation

Carbon nanotubes (CNTs) are used in various nano-electromechanical systems (NEMS), and the parameters (including the system parameters and the excitation parameters) may result in chaos in these systems. Thus, understanding the mechanism of the chaos arising from NEMS is vital for CNT’s applications. Motivated by this need, the chaotic properties of a single-walled carbon nanotube system resulting

This paper investigates chaos suppression in widely used indirect field oriented controlled induction machine (IFOCIM) drive system using fixed-time synergetic control method. The complex eighth-order IFOCIM drive system shows chaotic oscillations during a specific range of the integral gain of the PI speed controller. The conventional synergetic control method is improved by employing the fixed-time

In this paper, we consider a closed-loop supply chain (CLSC) consisting of two suppliers, one manufacturer, one risk-averse retailer and one fair-caring third-party in the presence of supply disruption. We focus on establishing a dynamic Stackelberg game model with bounded rational expectation and analyzing the game evolution process. The effects of key parameters on the Nash equilibrium solutions

In this paper, chaotic dynamics of a class of partial difference equations are investigated. With the help of the coupled-expansion theory of general discrete dynamical systems, two chaotification schemes for partial difference equations with polynomial maps are established. These controlled equations are proved to be chaotic either in the sense of Li–Yorke or in the sense of both Li–Yorke and Devaney

The timing of interventions plays a central role in managing and exploiting biological populations. However, few studies in the literature have addressed its effect on population stability. The Seno equation is a discrete-time equation that describes the dynamics of single-species populations harvested according to the proportional feedback method at any moment between two consecutive censuses. Here

A fractional-order model is proposed to describe the dynamic behaviors of the velocity of blood flow in cerebral aneurysm at the circle of Willis. The fractional-order derivative is used to model the blood flow damping term that features the viscoelasticity of the blood flow behaving between viscosity and elasticity, unlike the existing fractional models that use fractional-order derivatives to replace

Many natural phenomena can be modeled as discontinuous dynamical systems separated by a nonregular line. The number and distribution of limit cycles in discontinuous linear systems are important topics for research. In this paper, we focus on the limit cycles created by discontinuous planar piecewise linear systems separated by a nonregular line of center–center type, and prove that such systems have

An autonomous system of ordinary differential equations on the plane with a center-saddle bifurcation is considered. The influence of a class of time damped perturbations is investigated. The particular solutions tending to the fixed points of the limiting system are considered. The stability of these solutions is analyzed by Lyapunov function method when the bifurcation parameter of the unperturbed

A directed projection graph of the n-dimensional hypercube on the two-dimensional plane is successfully created. Any n-variable Boolean function can be easily transformed to an induced subgraph of the projection. Therefore, the discussions on n-variable Boolean functions only need to focus on a two-dimensional planar graph. Some mathematical theories on the projection graph and the induced subgraph

Two-dimensional unstable manifolds of the modified Chen system are constructed at equilibrium solution by “expanding up” along the unstable eigen-direction, hence it is tangent to the unstable eigenspace. In general, unstable manifold expands to the attraction basin of the corresponding limit cycle or attractor. With the introduction of time delay, the two-dimensional unstable manifold of an unstable

Using rigorous numerical methods, we prove the existence of 608 isolated periodic orbits in a gravitational billiard in a vibrating unbounded parabolic domain. We then perform pseudo-arclength continuation in the amplitude of the parabolic surface’s oscillation to compute large, global branches of periodic orbits. These branches are themselves proven rigorously using computer-assisted methods. Our

This paper focuses on the influence of two scales in the frequency domain on the behaviors of a typical dynamical system with a double Hopf bifurcation. By introducing an external periodic excitation to the normal form of the vector field with double Hopf bifurcation at the origin and taking the exciting frequency far less than the natural frequency, a theoretical model with two scales in the frequency

Bursting oscillations are ubiquitous in multi-time scale systems and have attracted widespread attention in recent years. However, research on experimental demonstration of the bursting oscillations induced by delayed bifurcation is very rarely reported. In this paper, a parametrically driven Rucklidge system is introduced and a distinct delayed behavior is observed when the time-varying parameter

We demonstrate in this paper a new chaotic behavior in the Lorenz system with periodically excited parameters. We focus on the parameters with which the Lorenz system has only two asymptotically stable equilibrium points, a saddle and no chaotic dynamics. A new mechanism of generating chaos in the periodically excited Lorenz system is demonstrated by showing that some trajectories can visit different

In this paper, the dynamics of a phytoplankton–zooplankton system with delay and diffusion are investigated. The positivity and persistence are studied by using the comparison theorem and upper and lower solutions method. The stability of steady states and the existence of local Hopf bifurcation are obtained by analyzing the distribution of eigenvalues. And the global existence of positive periodic

This paper mainly considers the complex dynamics of a discrete-time ring neural network with multiple time delays. By transforming the network system into a system of difference equations, one can obtain a chaotic neural network. More specifically, by projection method one can determine a closed invariant set of the system governed by some difference equations, and prove that some invariant subsystem

With the help of computer algebra system-Mathematica, this paper considers the weak center problem and local critical periods for bi-center of a Z2-equivariant quintic system with eight parameters. The order of weak bi-center is identified and the exact maximum bifurcation number of critical periods generated from the bi-center is given via the combination of symbolic calculation and numerical analysis

In this study, a chaos-theoretic method is proposed to model the case of ferroresonance that can occur under nominal conditions in power systems, and the factors that determine the types of ferroresonance to occur are examined. In the ferroresonance chaotic system modeled in Matlab environment, the length of the transmission line and the breaker capacities in the circuit are fixed and its relationship

We propose a nonsmooth Filippov refuge ecosystem with a piecewise saturating response function and analyze its dynamics. We first investigate some key elements to our model which include the sliding segment, the sliding mode dynamics and the existence of equilibria which are classified into regular/virtual equilibrium, pseudo-equilibrium, boundary equilibrium and tangent point. In particular, we consider

In this paper, we introduce a new concept, (α,β)-mean Li–Yorke chaotic operator, which includes the standard mean Li–Yorke chaotic operators as special cases. We show that when α<1≤β or α≤1<β, (α,β)-mean Li–Yorke chaotic dynamics is strictly stronger than the ones that appeared in mean Li–Yorke chaos. When α>1 or β<1, it has completely different characteristics from the mean Li–Yorke chaos. We prove

In recently published work [Inaba & Kousaka, 2020a; Inaba & Tsubone, 2020b], we discovered significant mixed-mode oscillation (MMO) bifurcation structures in which MMOs are nested. Simple mixed-mode oscillation-incrementing bifurcations (MMOIBs) are known to generate [A0,B0×n] oscillations for successive n between regions of A0- and B0-oscillations, where A0 and B0 are adjacent simple MMOs, e.g. A0=1s

In this paper, a new impact-to-impact mapping is constructed to investigate the stochastic response of a nonautonomous vibro-impact system. The significant feature lies in the choice of Poincaré section, which consists of impact surface and codimensional time. Firstly, we construct a new impact-to-impact mapping to calculate the one-step transition probability matrix from a given impact to the next

A chaotic system that can show multiscroll and megastable attractors is studied in this paper. Two cases of the system with periodic and quasi-periodic excitations are discussed. Various stabilities of the system determined by changing parameters and initial values are investigated for both cases. In Case-A of the proposed system, multiscroll attractors are shown for the various parameter values. In

In this paper, we consider a viral infection dynamics model with immune impairment and time delay in immune expansion. By calculation, it is shown that the model has three equilibria: infection-free equilibrium, immunity-inactivated infection equilibrium, and immunity-activated infection equilibrium. By analyzing the distributions of roots of corresponding characteristic equations, the local stability

In this paper, a cryptanalysis method that combines a chosen-ciphertext attack with a divide-and-conquer attack by traversing multiple nonzero component initial conditions (DCA-TMNCIC) is proposed. The method is used for security analysis of n-D (n=3,4,5,6,7,8) self-synchronous chaotic stream ciphers that employ a product of two chaotic variables and three chaotic variables (n-D SCSC-2 and n-D SCSC-3)

In this paper, we explore the dynamical behaviors of the 1D two-grid coupled cellular neural networks. Assuming the boundary conditions of zero-flux type, the stability of the zero equilibrium is discussed by analyzing the relevant eigenvalue problem with the aid of the decoupling method, and the conditions for the occurrence of Turing instability and Hopf bifurcation at the zero equilibrium are derived

For a shallow water model with Coriolis effect, by applying the methodologies of dynamical systems and singular traveling wave theory developed by Li and Chen [2007] to its traveling wave system, under different parameter conditions, all possible bounded solutions (solitary wave solution, pseudo-peakon and periodic peakons as well as compactons) are obtained. Some exact explicit parametric representations

Balanced colorings of networks classify robust synchrony patterns — those that are defined by subspaces that are flow-invariant for all admissible ODEs. In symmetric networks, the obvious balanced colorings are orbit colorings, where colors correspond to orbits of a subgroup of the symmetry group. All other balanced colorings are said to be exotic. We analyze balanced colorings for two closely related

Memristive technologies are attractive due to their nonvolatility, high density, low power, nanoscale geometry, nonlinearity, binary/multiple memory capacity, and negative differential resistance. For memristive devices, a model corresponding with practical behavioral characteristics is highly favorable for the realization of its neuromorphic system and applications. In this paper, we propose a novel

The nonlinear dynamical behaviors of economic models have been extensively examined and still represented a great challenge for economists in recent and future years. A proposed boundedly rational game incorporating consumer surplus is introduced. This paper aims at studying stability and bifurcation types of the presented model. The flip and Neimark–Sacker bifurcations are analyzed via applying the

A delayed three-component reaction–diffusion system with weak Allee effect and Dirichlet boundary condition is considered. The existence and stability of the positive spatially nonhomogeneous steady-state solution are obtained via the implicit function theorem. Moreover, taking delay as the bifurcation parameter, the Hopf bifurcation near the spatially nonhomogeneous steady-state solution is proved

Memristor, as a nonlinear element in nanometer size, is feasible to generate chaotic signals. Especially, it can improve the randomness of the signals and the complexity of chaotic systems. A novel multiscroll hyperchaotic system based on the flux-controlled memristor is designed. Its twin system with a different topological structure is obtained by varying only the flux variable of the memristor,

Dynamical systems generated by continuous maps on compact metric spaces can have various properties, e.g. the existence of an arc horseshoe, the positivity of topological entropy, the existence of a homoclinic trajectory, the existence of an omega-limit set containing two minimal sets and other. In [Kočan et al., 2014] we consider six such properties and survey the relations among them for the cases

The estimate of the ultimate bound for a dynamical system is an important problem, which is useful for chaos control and synchronization. In this paper, the estimated ultimate bound of a class of complex Lorenz systems is provided, which extends the parameter regions identified in the current literature on this problem. Based on these results, a kind of complex Lorenz-type systems is constructed, which

Public awareness programs may deeply influence the epidemic pattern of a contagious disease by altering people’s perception of risk and individuals behavior during the course of the epidemic outbreak. Regardless of the veracity, social media advertisements are expected to execute an increasingly prominent role in the field of infectious disease modeling. In this paper, we propose a model which portrays

In the paper, the theoretical study on some experimental and numerical results of grazing bifurcation for a soft impacting system are analyzed. After the conditions under which nonimpact period-1 orbit and grazing bifurcation exist are given, we prove that an impact period-1 orbit exists by the implicit function theorem. The details of these periodic orbits are also investigated, which also helps us

In this paper, a p53-Mdm2 mathematical model is analyzed to understand the biological implications of feedback loops in a p53 system. Results show that the model can undergo four types of codimension-3 Bogdanov–Takens bifurcations, including cusp, saddle, focus and elliptic. Specifically, we find new phenomena including the coexistence of four positive equilibria, two limit cycles, the coexistence

Little is known about bifurcations in two-dimensional (2D) differential systems from the viewpoint of Kosambi–Cartan–Chern (KCC) theory. Based on the KCC geometric invariants, three types of static bifurcations in 2D differential systems, i.e. saddle-node bifurcation, transcritical bifurcation, and pitchfork bifurcation, are discussed in this paper. The dynamics far from fixed points of the systems

The paper concludes the series of the research works on the interdisciplinary analytical approach (the so-called bifurcation-fractal analytics) to forecast the dynamics of pulse systems on the basis of modified bifurcation diagrams. These diagrams are intended to integrate incompatible-in-traditional-spaces images (mainly transients from the phase space and evolution pictures from the parametric space)

By adding trend followers, we extend the model given by Tramontana et al. from one-dimensional (1D) piecewise linear discontinuous (PWLD) map to a new 2D PWLD map. Using this map in financial markets, we describe the bifurcation mechanisms associated with the appearance/disappearance of cycles, which may be related to several cases: border collision bifurcations; Poincaré equator collision bifurcations;

Improving running-in quality is an important project of Green Tribology. In actual environment, the running-in quality of mechanical equipment is greatly affected by system parameters. In view of this, running-in experiments were performed at different rotating speeds on a pin-on-disc tribometer. Chaos theory was used to investigate the effect of rotating speeds on the running-in quality. The experimental

We show the existence and properties of an exact universal excitation waveform for optimal enhancement of directed ratchet transport (in the sense of the average velocity) by providing three alternative derivations. Specifically, it is deduced from the criticality scenario giving rise to ratchet universality as well as from an approach based on Fokker–Planck’s equation. Numerical experiments confirmed

In this paper, a family of quasiperiodically forced piecewise linear maps is considered. It is proved that there exists a unique strange nonchaotic attractor for some set of parameter values. It is the graph of an upper semi-continuous function, which is invariant, discontinuous almost everywhere and attracts almost all orbits. Moreover, both Lyapunov exponents on the attractor is nonpositive. Finally

Slow–fast dynamical systems, i.e. singularly or nonsingularly perturbed dynamical systems possess slow invariant manifolds on which trajectories evolve slowly. Since the last century various methods have been developed for approximating their equations. This paper aims, on the one hand, to propose a classification of the most important of them into two great categories: singular perturbation-based

The deterministic chaos in the sense of a positive topological entropy is investigated for differential equations with multivalued impulses. Two definitions of topological entropy are examined for three classes of multivalued maps: n-valued maps, Rδ-maps and admissible maps in the sense of Górniewicz. The principal tool for its lower estimates and, in particular, its positivity are the Ivanov-type

There is now much geological evidence that the Earth was fully glaciated during several periods in the geological past (about 700Myr ago) and attained a so-called Snowball Earth (SBE) state. Additional support for this idea has come from climate models of varying complexity that show transitions to SBE states and undergo hysteresis under changes in solar radiation. In this paper, we apply large-scale

This paper presents a novel current-controlled locally-active memristor model to reveal the switching and oscillating characteristics of locally-active devices. It is shown that the memristor has two asymptotically stable equilibrium points on its power-off plot and therefore exhibits nonvolatility. Switching from one stable equilibrium point to another is achieved by applying a suitable current pulse

We consider complex networks where the dynamics of each interacting agent is given by a nonlinear vector field and the connections between the agents are defined according to the topology of undirected simple graphs. The aim of the work is to explore whether the asymptotic dynamic behavior of the entire network can be fully determined from the knowledge of the dynamic properties of the underlying constituent

The analytical studies and chaotic behavior of forced vibration on Single-wall Carbon Nanotubes (SWCNTs) embedded in nonlinear viscous elastic medium subjected to parametric excitation are investigated. The analytical solution of the amplitude of nonlinear vibration is studied using Krylov–Bogoliubov–Mitropolsky (KBM) method. Both resonant and nonresonant cases are deduced. The computational techniques

The pulse-shaped explosion (PSE), characterized by the pulse-shaped quantitative of system solutions varying dramatically, is a special route to bursting oscillations reported recently. This paper reports interesting dynamical behaviors related to the PSE of equilibria, and based on that, the complex bursting dynamics is investigated in a van der Pol–Mathieu–Duffing system with multiple-frequency slow-varying

We provide the normal forms, the bifurcation diagrams and the global phase portraits on the Poincaré disk of all planar Kukles systems of degree 3 with ℤ2-symmetries.