相关论文: Synthesizing attractors of Hindmarsh-Rose neuronal…

This paper presents a simple periodic parameter-switching method which can find any stable limit cycle that can be numerically approximated in a generalized Duffing system. In this method, the initial value problem of the system is…

In this paper the attractors synthesis algorithm for a class of dissipative dynamical systems with hyperbolic equilibria, presented in [1], is applied to generate any attractor of the Rikitake system. By switching periodically, or even…

The review presents a parameter switching algorithm and his applications which allows numerical approximation of any attractor of a class of continuous-time dynamical systems depending linearly on a real parameter. The considered classes of…

For stochastic Hindmarsh-Rose equations with additive noises in the study of neurodynamics, the longtime and global pullback dynamics on a two-dimensional bounded domain is explored in this work. Using the additive transformation and by the…

Problems with artificial neural networks originate from their deterministic nature and inevitable prior learnings, resulting in inadequate adaptability against unpredictable, abrupt environmental change. Here we show that a stochastically…

The longtime and global pullback dynamics of stochastic Hindmarsh-Rose equations with multiplicative noise on a three-dimensional bounded domain in neurodynamics is investigated in this work. The existence of a random attractor for this…

In this letter we synthesize numerically the L\"{u} attractor starting from the generalized Lorenz and Chen systems, by switching the control parameter inside a chosen finite set of values on every successive adjacent finite time intervals.…

In this paper, the problem of approximating hidden chaotic attractors of a general class of nonlinear systems is investigated. The Parameter Switching (PS) algorithm is utilized, which switches the control parameter within a given set of…

In this paper, the Parameter Switching (PS) algorithm is used to approximate numerically attractors of a Hopfield Neural Network (HNN) system. The PS algorithm is a convergent scheme designed for approximating attractors of an autonomous…

We observe the occurrence of a strange nonchaotic attractor in a periodically driven two-dimensional map, formerly proposed as a neuron model and a sequence generator. We characterize this attractor through the study of the Lyapunov…

In this paper the dynamics of an autonomous mathematical models of COVID-19 depending on a real parameter bifurcation, is controlled by switching periodically the parameter value. For this purpose the Parameter Switching (PS) algorithm is…

We study the dynamical properties of a broad class of high-dimensional random dynamical systems exhibiting chaotic as well as fixed point and periodic attractors. We consider cases in which attractors can co-exists in some regions of the…

Attractor neural network models of cortical decision-making circuits represent them as dynamical systems in the state space of neural firing rates with the attractors of the network encoding possible decisions. While the attractors of these…

In this paper we show how the Parameter Switching algorithm, utilized initially to approximate attractors of a general class of nonlinear dynamical systems, can be utilized also as a synchronization-induced method. Two illustrative examples…

A succesful method to describe the asymptotic behavior of a discrete time stochastic process governed by some recursive formula is to relate it to the limit sets of a well chosen mean differential equation. Under an attainability condition,…

The existence of an exponential attractor for the diffusive Hindmarsh-Rose equations on a three-dimensional bounded domain originated in the study of neurodynamics is proved through uniform estimates together with a new theorem on the…

The random map model is a deterministic dynamical system in a finite phase space with n points. The map that establishes the dynamics of the system is constructed by randomly choosing, for every point, another one as being its image. We…

It is shown that the time-averaged dynamics of memristors and their networks periodically driven by alternating-polarity pulses may converge to fixed-point attractors. Starting with a general memristive system model, we derive basic…

This work explores a synchronization-like phenomenon induced by common noise for continuous-time Markov jump processes given by chemical reaction networks. A corresponding random dynamical system is formulated in a two-step procedure, at…

Common experience suggests that attracting invariant sets in nonlinear dynamical systems are generally stable. Contrary to this intuition, we present a dynamical system, a network of pulse-coupled oscillators, in which \textit{unstable…