Journal ArticleDOI
Stability switches and Bogdanov-Takens bifurcation in an inertial two-neuron coupling system with multiple delays
Zigen Song,Jian Xu +1 more
TLDR
In this paper, the authors investigate an inertial two-neural coupling system with multiple delays and find that multiple delays can induce the system to exhibit stable switching between the resting state and periodic motion.Abstract:
In this paper, we investigate an inertial two-neural coupling system with multiple delays. We analyze the number of equilibrium points and demonstrate the corresponding pitchfork bifurcation. Results show that the system has a unique equilibrium as well as three equilibria for different values of coupling weights. The local asymptotic stability of the equilibrium point is studied using the corresponding characteristic equation. We find that multiple delays can induce the system to exhibit stable switching between the resting state and periodic motion. Stability regions with delay-dependence are exhibited in the parameter plane of the time delays employing the Hopf bifurcation curves. To obtain the global perspective of the system dynamics, stability and periodic activity involving multiple equilibria are investigated by analyzing the intersection points of the pitchfork and Hopf bifurcation curves, called the Bogdanov-Takens (BT) bifurcation. The homoclinic bifurcation and the fold bifurcation of limit cycle are obtained using the BT theoretical results of the third-order normal form. Finally, numerical simulations are provided to support the theoretical analyses.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
Exponential H ∞ filtering analysis for discrete-time switched neural networks with random delays using sojourn probabilities
TL;DR: In this paper, the authors considered a class of discrete-time switched neural networks with random time-varying delays based on the sojourn-probability-dependent method using the average dwell time approach together with the piecewise Lyapunov function technique.
Journal ArticleDOI
Transition of electric activity of neurons induced by chemical and electric autapses
TL;DR: The results confirm that chemical autapse can enhance and/or suppress the transition of electric activity with excitable or inhibitory type driven by electric autapse, vice versa and indicates that an appropriate switch-off-on for autapses can make the neuron give different types of response to external forcing.
References
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