Stochastic resonance in a discrete neuron with time delay and two different modulation signals

Wang, Can Jun; Yang, Ke; Qu, Shi Xian

doi:10.1088/0031-8949/89/10/105001

Cited by 16 publications

(3 citation statements)

References 40 publications

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“…[37] Other similar studies on single neurons with time delay can be found in Refs. [38][39][40]. While for neural network constructed with multiple neurons, time delay plays a subtle role in either promoting or impeding synchronization.…”

Section: Introductionmentioning

confidence: 99%

Hopf bifurcation and phase synchronization in memristor-coupled Hindmarsh–Rose and FitzHugh–Nagumo neurons with two time delays

Guo¹,

Li²,

Wang³

et al. 2023

Chinese Phys. B

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In this study, a memristor-coupled heterogenous neural network consisting of two-dimensional (2D) FitzHugh–Nagumo (FHN) and Hindmarsh–Rose (HR) neurons with two time delays is established. Taking the time delays as the control parameters, the existence of Hopf bifurcation near the stable equilibrium point in four cases is derived theoretically, and the validity of the Hopf bifurcation condition is verified by numerical analysis. The results shows that the two time delays can make the stable equilibrium point unstable, thus leading to periodic oscillations induced by Hopf bifurcation. Furthermore, the time delays in FHN and HR neurons have different effects on the firing activity of neural network. Complex firing patterns, such as quiescent state, chaotic spiking and periodic spiking can be induced by the time delay in FHN neuron, while the neural network only exhibits quiescent state and periodic spiking with the change of the time delay in HR neuron. Especially, phase synchronization between the heterogeneous neurons is explored, and the results show that the time delay in HR neurons has a greater effect on blocking the synchronization than the time delay in FHN neuron. Finally, the theoretical analysis is verified by circuit simulations.

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Section: Introductionmentioning

confidence: 99%

Hopf bifurcation and phase synchronization in memristor-coupled Hindmarsh–Rose and FitzHugh–Nagumo neurons with two time delays

Guo¹,

Li²,

Wang³

et al. 2023

Chinese Phys. B

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“…They have showed that presence of delay in the system exhibits more complicated dynamics than the non-delayed one. The effects of time delay on stochastic system have been investigated by many researchers [12][13][14][15]. More recently, the influences of time delay in stochastic insect outbreak model has been investigated [16].…”

Section: Introductionmentioning

confidence: 99%

Delay induced dynamical behaviors in a stochastic insect outbreak model in presence of Michaelis-Menten type harvesting

Mandal¹,

Poria

2021

Phys. Scr.

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In this paper, we have considered stochastic insect outbreak model in presence of Michaelis-Menten type of harvesting. The growth of the insect species is taken as delayed logistic type together with a multiplicative noise term. The impact of internal environmental disturbances on the insect population is taken into account by adding an additive noise term in the model. The effects of the noises, cross correlation strength of the noises and time delay on the insect population are investigated and observed very rich dynamical behaviors. It is ascertained that multiplicative noise reduces population size greatly than additive noise. As usual, increase of harvesting of insect species reduces the population size at faster rate. Regime shift is possible depending on multiplicative noise only in contrast it is not possible via only additive noise. One of the key finding is the noise-delayed switching phenomenon for negatively correlated noises.

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“…Time delay is an important factor affecting the dynamical behavior of the systems, and even makes the system unstable. Therefore, the dynamical behavior of time-delayed systems has attracted considerable attention in various fields [26][27][28][29][30]. Time-delayed chaotic systems have more complex and abundant dynamics and are more suitable for some engineering applications, such as secure communication [31][32][33].…”

Section: Introductionmentioning

confidence: 99%

Combined projective synchronization for a class of time-delayed hyperchaotic systems via active control

2019

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We investigate combined projective synchronization for a class of time-delayed chaotic systems related to optical bistable or hybrid optical bistable devices. We overcome some limitations of previous works, where only combined complete synchronization can be achieved. Based on the Lyapunov asymptotical stability theory and active control technology, the effective sufficient conditions derived to ensure the combined projective synchronization for a class of time-delayed hyperchaotic systems can be investigated. The efficiency and effectiveness of the proposed method have been verified with several numerical simulations using well-known time-delayed chaotic systems.

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Stochastic resonance in a discrete neuron with time delay and two different modulation signals

Cited by 16 publications

References 40 publications

Hopf bifurcation and phase synchronization in memristor-coupled Hindmarsh–Rose and FitzHugh–Nagumo neurons with two time delays

Hopf bifurcation and phase synchronization in memristor-coupled Hindmarsh–Rose and FitzHugh–Nagumo neurons with two time delays

Delay induced dynamical behaviors in a stochastic insect outbreak model in presence of Michaelis-Menten type harvesting

Combined projective synchronization for a class of time-delayed hyperchaotic systems via active control

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