Journal ArticleDOI
Bifurcation analysis for Hindmarsh-Rose neuronal model with time-delayed feedback control and application to chaos control
TLDR
In this paper, the authors adopt the time-delayed feedback control, and convert chaos control to the Hopf bifurcation of the delayed feedback system, showing that the excitable neuron can emit spikes via the subcritical Hopf Bifurcation, and exhibits periodic or chaotic spiking/bursting behaviors with the increase of external current.Abstract:
This paper is concerned with bifurcations and chaos control of the Hindmarsh-Rose (HR) neuronal model with the time-delayed feedback control. By stability and bifurcation analysis, we find that the excitable neuron can emit spikes via the subcritical Hopf bifurcation, and exhibits periodic or chaotic spiking/bursting behaviors with the increase of external current. For the purpose of control of chaos, we adopt the time-delayed feedback control, and convert chaos control to the Hopf bifurcation of the delayed feedback system. Then the analytical conditions under which the Hopf bifurcation occurs are given with an explicit formula. Based on this, we show the Hopf bifurcation curves in the two-parameter plane. Finally, some numerical simulations are carried out to support the theoretical results. It is shown that by appropriate choice of feedback gain and time delay, the chaotic orbit can be controlled to be stable. The adopted method in this paper is general and can be applied to other neuronal models. It may help us better understand the bifurcation mechanisms of neural behaviors.read more
Citations
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Journal ArticleDOI
Multiple modes of electrical activities in a new neuron model under electromagnetic radiation
TL;DR: It is found that the electromagnetic radiation can excite quiescent neuron but also can suppress the electrical activities in neuron as well, and these results are consistent with biological experiments.
Journal ArticleDOI
A review for dynamics of collective behaviors of network of neurons
TL;DR: In this review, the dynamics for neuron, neuronal network is introduced, for example, the mode transition in electrical activity, functional role of autapse connection, bifurcation verification in biological experiments, interaction between neuron and astrocyte, noise effect, coherence resonance, pattern formation and selection in network of neurons.
Journal ArticleDOI
A novel memristive neural network with hidden attractors and its circuitry implementation
TL;DR: Interestingly, the memristive neural network can generate hyperchaotic attractors without the presence of equilibrium points and circuital implementation of such memristives is presented to show its feasibility.
Journal ArticleDOI
Three-Dimensional Memristive Hindmarsh–Rose Neuron Model with Hidden Coexisting Asymmetric Behaviors
TL;DR: A novel three-dimensional memristive Hindmarsh–Rose (HR) neuron model is presented in this paper to describe complex dynamics of neuronal activities with electromagnetic induction and can show hidden dynamical behaviors of coexisting asymmetric attractors.
Journal ArticleDOI
Lévy noise induced stochastic resonance in an FHN model
ZhanQing Wang,Yong Xu,Hui Yang +2 more
TL;DR: In this paper, the authors investigated the stochastic resonance in an FHN model with an additive Levy noise numerically, which is a kind of general random noise which is different from the usual Gaussian noise.
References
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Synchronization: A Universal Concept in Nonlinear Sciences
TL;DR: This work discusseschronization of complex dynamics by external forces, which involves synchronization of self-sustained oscillators and their phase, and its applications in oscillatory media and complex systems.
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TL;DR: One-Parameter Bifurcations of Equilibria in continuous-time systems and fixed points in Discrete-Time Dynamical Systems have been studied in this paper, where they have been used for topological equivalence and structural stability of dynamical systems.
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