The Cardiac Purkinje Fiber (CPF) is the last branch of the heart conduction system, which is meshed with the normal ventricular myocyte. Purkinje fiber plays a key role in the occurrence of ventricular arrhythmia and maintenance. Does the heart Purkinje fiber cells have the same memory function as the cerebral nerve? In this paper, the cardiac Hodgkin–Huxley equation is taken as the object of study

The curse of dimensionality looms over many studies in science and engineering. Low-order systems provide conceptual clarity but often fail to reveal the extent of possible complexity, whereas high-order systems present a host of daunting challenges to the analyst, not least the classification and visualization of typical behavior. In this paper, we detail the behavior of systems that fall somewhere

We characterize the dynamical states of a piezoelectric micrcoelectromechanical system (MEMS) using several numerical quantifiers including the maximum Lyapunov exponent, the Poincaré Surface of Section and a chaos detection method called the Smaller Alignment Index (SALI). The analysis makes use of the MEMS Hamiltonian. We start our study by considering the case of a conservative piezoelectric MEMS

The goal of this paper is to apply the method of Lagrangian descriptors to reveal the phase space mechanism by which a Caldera-type potential energy surface (PES) exhibits the dynamical matching phenomenon. Using this technique, we can easily establish that the nonexistence of dynamical matching is a consequence of heteroclinic connections between the unstable manifolds of the unstable periodic orbits

We study numerically the α- and ω-limits of the Newton maps of quadratic polynomial transformations of the plane into itself. Our results confirm the conjectures posed in a recent work about the general dynamics of real Newton maps on the plane.

From [Han et al., 2009a] we know that the highest order of the nilpotent center of cubic Hamiltonian system is 3. In this paper, perturbing the Hamiltonian system which has a nilpotent center of order 3 at the origin by cubic polynomials, we study the number of limit cycles of the corresponding cubic near-Hamiltonian systems near the origin. We prove that we can find seven and at most seven limit cycles

The main aim of this paper is to study the oscillatory behaviors of gene expression networks in quorum-sensing system with time delay. The stability of the unique positive equilibrium and the existence of Hopf bifurcation are investigated by choosing the time delay as the bifurcation parameter and by applying the bifurcation theory. The explicit criteria determining the direction of Hopf bifurcation

In this paper, we describe a coupled nonlinear electromechanical torsional vibration model of a high-speed permanent magnet synchronous motor driven system based on the Lagrange–Maxwell theory. The chaotic state is induced by external excitation forces. A multitime delay feedback control scheme is derived to suppress chaos in such vibrations. An analytical criterion condition for chaos is deduced by

In this paper, we consider a predator–prey system with Holling type III ratio-dependent functional response. Such a system can exhibit complex dynamical behavior such as bistable and tristable phenomena which contain equilibria and oscillating motions for certain parameter values. In particular, we show that the ratio-dependent predator–prey system can exhibit multiple limit cycles due to Hopf bifurcation

In this paper, we extend the equivariant Hopf bifurcation theory for semilinear functional differential equations in general Banach spaces and then apply it to reaction–diffusion models with delay effect and homogeneous Dirichlet boundary condition on a general open domain with a smooth boundary. In the process we derive the criteria for the existence and directions of branches of bifurcating periodic

The nonlinear response of neuron firing under external electromagnetic radiation as well as transmembrane current, as two kinds of external forces, are studied in an improved Fitzhugh–Nagumo (FHN) model. The control effects of external forces to neuron firing are measured by winding number Ω during mode transition of motion types. The phenomenon of match and mismatch between the angular frequency ωout

In this paper, we investigate discontinuous bifurcations of a soft-impact system, which is nonsmooth at the switching boundary consisting of two parts. We find that there are no periodic orbits located only in the impact zone, and when grazing bifurcation on one part of the switching boundary occurs, the tangency point changes may occur for different bifurcation parameters, which is also verified by

In this paper, we consider the realization of configuration of limit cycles of piecewise linear systems on the plane. We show that any configuration of finite number of Jordan curves can be realized by a discontinuous piecewise linear system with two zones separated by a continuous curve.

The dynamic behavior of the tumor suppressor p53 as an important signal in response to various stresses can influence cellular fate decisions. Programmed cell death 5 (PDCD5) and wild type p53-induced phosphatase 1 (Wip1) regulate p53 dynamics as its activator and inhibitor, respectively. In the present study, we add Wip1 to p53-Mdm2 (Murine double minute 2) module with PDCD5 and focus on p53 dynamics

The motion of the pendulum in a variable sawtooth force field is considered. For the “lower” equilibrium, the necessary stability conditions are investigated numerically, the results are presented in the form of an Ince–Strutt diagram. Using the Poincaré–Melnikov method separatrix splitting is studied analytically. Numerically, for some values of parameters, the nonlinear dynamics is studied using

We explore the impact of time-periodic forcing on pattern transitions in a plankton system of reaction–diffusion type. Here, we mainly focus on the forced states near the Turing–Hopf bifurcation. A normal form analysis leads to the finding that weak forcing exhibits a destabilizing effect on the dynamics by exciting the transitions from a spatially homogeneous stationary state to a periodic oscillation

In this paper, we are concerned with a diffusive predator–prey model where the functional response follows the predator cooperation in hunting and the growth of the prey obeys the Allee effect. Firstly, the existence and stability of the positive equilibrium are explicitly determined by the local system parameters. It is shown that the ability of the hunting cooperation can affect the existence of

In this paper, we consider a simple equation which involves a parameter k, and its traveling wave system has a singular line. Firstly, using the qualitative theory of differential equations and the bifurcation method for dynamical systems, we show the existence and bifurcations of peak-solitary waves and valley-solitary waves. Specially, we discover the following novel properties: (i) In the traveling

In this paper, the method of dynamical systems developed in [Li & Chen, 2007] is applied to the rotation-two-component Camassa–Holm system. Through qualitative analysis, under given parameter conditions, exact explicit solitary wave solution, pseudo-peakon solution, peakon and periodic peakon, as well as compacton solution, are obtained. Some parameter conditions constraints are derived for ensuring

A singularity theory, in the form of path formulation, is developed to analyze and organize the qualitative behavior of multiparameter ℤ2-equivariant bifurcation problems of corank 2 and their deformations when the trivial solution is preserved as parameters vary. Path formulation allows for an efficient discussion of different parameter structures with a minimal modification of the algebra between

A memristor with coexisting pinched hysteresis loops and twin local activity domains is presented and analyzed, with an emulator being designed and applied to the classic Chua’s circuit to replace the diode. The memristive system is modeled with four coupled first-order autonomous differential equations, which has three equilibria determined by three static equilibria of the memristor but not controlled

We are concerned with the Turing instability and pattern caused by cross-diffusion in a strongly coupled spatial predator–prey system. We explore how cross-diffusion destabilizes the spatially uniform steady state which is stable in reaction–diffusion systems, and explicitly describe the Turing space under certain conditions. Particularly, when the parameter values are taken in the Turing–Hopf domain

Following the scheme inspired by Tsallis [Jagannathan & Sudeshna, 2005; Patidar & Sud, 2009], we study the Gaussian map and its q-deformed version. We compute the topological entropies of the discrete dynamical systems which are obtained for both maps, the original Gaussian map and its q-modification. In particular, we are able to obtain the parametric region in which the topological entropy is positive

The ionization of hydrogen in a circularly polarized electric field consists of the electron escaping over a rotating Stark saddle. The escape is mediated by the stable and unstable manifolds of a normally hyperbolic invariant manifold associated with the saddle. General principles guarantee the existence of this normally hyperbolic invariant manifold which is referred to as a transition state for

This study investigates the behavior of a damped, inelastic, sinusoidally forced impact oscillator which has its barrier placed such that the oscillator always vibrates under compression about its subharmonic resonant frequencies. The Poincaré sections at near subharmonic resonance conditions exhibit finger-shaped chaotic attractors, similar to the strange attractor mapping of Hénon and the ones found

The generalized Hamiltonian function is proposed for the brushless DC motor (BLDCM) chaotic system. The Hamiltonian and Casimir functions are derived from the generalized Hamiltonian function. In this way the Casimir energy is proven to be a special type of the generalized Hamiltonian function. The derivative of the Hamiltonian function is used for analyzing the various dynamical behaviors under different

In this paper, a prey–predator-top predator food chain model with nonmonotonic functional response in the predators is studied. With an emphasis on the nutrition conversion rate of predator to top predator, one can get two important thresholds: the top predator extinction threshold and the coexistence threshold. The top predator will die out if the nutrition conversion rate of predator to top predator

In this paper, a predator–prey model with age structure in predator is studied. Using maturation period as the varying parameter, we prove the existence of Hopf bifurcation for the model and calculate the bifurcation properties, such as the direction of Hopf bifurcation and the stability of bifurcated periodic solutions. The method we employed includes Hopf bifurcation theorem, center manifolds and

In this paper, we study a class of Zp-equivariant planar polynomial differential systems ż=(a+i)z+(b+i)z|z|2(p−2)+cz|z|2−5i2z¯p−1. It is shown that for any 4≤p∈ℕ there is a differential system of the above type having at least 2p limit cycles. This is proved by estimating the number of zeros of the first-order Melnikov function.

One of the main applications for chaotic circuits is the production of aperiodic signals with many of the characteristics of noise for secure communications and similar uses. However, the probability distribution function (pdf) of such signals is usually far from Gaussian. This paper describes a new chaotic circuit based on the recently proposed signum thermostat that produces signals whose pdf is

In this work, by using an algebraic criterion presented by us in an earlier paper, we determine the conditions on the parameters in order to guarantee the nonchaotic behavior for some classes of nonlinear third-order ordinary differential equations of the form x...=j(x,ẋ,ẍ), called jerk equations, where j is a polynomial of degree n. This kind of equation is often used in literature to study chaotic

Driver fatigue has caused numerous vehicle crashes and traffic injuries. Exploring the fatigue mechanism and detecting fatigue state are of great significance for preventing traffic accidents, and further lessening economic and societal loss. Due to the objectivity of EEG signals and the availability of EEG acquisition equipment, EEG-based fatigue detection task has raised great attention in recent

This paper investigates the problem of searching for the robust initial values of noisy fractional-order chaotic systems when the desired output is given. The problem is addressed under the framework of robust evolutionary optimization. Two different ways of adding noise are considered: (1) the noise is added to the initial point; (2) the noise is added to the orbit of the system. A series of experiments

Re-emergence of cholera threatens people’s health globally. However, its periodic re-emerging outbreaks are still poorly understood. In this paper, we develop a simple ordinary differential equation (ODE) model to study the cholera outbreak cycles. Our model involves both direct (i.e. human-to-human) and indirect (i.e. environment-to-human) transmission routes, due to the multiple interactions between

In this paper, the amplitude equations of a Gray–Scott model without (or with) the feedback time delay are derived based on weakly nonlinear method, by which the selection of Turing patterns for this model can be theoretically determined. As a result, the effects of the diffusion coefficient ratio and the time delay factor on the Turing pattern can be investigated as the main purpose of this paper

Some characteristics of mean sensitivity and Banach mean sensitivity using Furstenberg families and inverse limit dynamical systems are obtained. The iterated invariance of mean sensitivity and Banach mean sensitivity are proved. Applying these results, the notion of mean sensitivity and Banach mean sensitivity is extended to uniform spaces. It is proved that a point-transitive dynamical system in

Synchronization in complex networks is an evergreen subject with many practical applications across the natural and social sciences. The stability of synchronization is thereby crucial for determining whether the dynamical behavior is stable or not. The master stability function is commonly used to that effect. In this paper, we study whether there is a relation between the stability of synchronization

In this article using an analytical method called Fishing principle we obtain the region of parameters, where the existence of a homoclinic orbit to a zero saddle equilibrium in the Lorenz-like system is proved. For a qualitative description of the different types of homoclinic bifurcations, a numerical analysis of the obtained region of parameters is organized, which leads to the discovery of new

We investigate the effect of a memristive element on the dynamics of a chaotic system. For this purpose, the chaotic Chua’s oscillator is extended by a memory element in the form of a double-barrier memristive device. The device consists of Au/NbOx/Al2O3/Al/Nb layers and exhibits strong analog-type resistive changes depending on the history of the charge flow. In the obtained system we observe strong

We obtain necessary and sufficient conditions for the existence of a center on a local center manifold for three 4-parameter families of quadratic systems on ℝ3. We also give a positive answer to an open question posed in [Dias & Mello(2010)] related to similar systems.

Inferior olive (IO) neurons project to the cerebellum and contribute to motor control. They can show intriguing spatio-temporal dynamics with rhythmic and synchronized spiking. IO neurons are connected to their neighbors via gap junctions to form an electrically coupled network, and so it is considered that this coupling contributes to the characteristic dynamics of this nucleus. Here, we demonstrate

Binocular rivalry is a useful experimental paradigm to investigate aspects of neocortical dynamics related to conscious perception. Frequency-tagged EEG responses to a sine-flickered visual stimulus were contrasted between episodes of perceptual dominance, i.e., conscious perception of that stimulus and perceptual nondominance, i.e., conscious perception of a rival stimulus presented at a different

The spontaneous breakup of a single spiral wave of excitation into a turbulent wave pattern has been observed in both discrete element models and continuous reaction-diffusion models of spatially homogeneous 2D excitable media. These results have attracted considerable interest, since spiral breakup is thought to be an important mechanism of transition from the heart rhythm disturbance ventricular