Stochastic resonance in FitzHugh–Nagumo system with time-delayed feedback

Wu, Dan; Zhu, Shiqun

doi:10.1016/j.physleta.2008.06.015

Cited by 51 publications

(19 citation statements)

References 49 publications

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“…Proof See Appendix A. Remark Obviously,

(∥∥, \overset{h}{true} (t)) = (∥∥, \frac{h (t) x^{T} e}{((), (∥∥, h (t) x^{T} e) + γ)}) \leq τ < 1

. If γ = 0, then

(∥∥, \frac{h (t) x^{T} e}{((), (∥∥, h (t) x^{T} e) + γ)}) = 1

, it is not consistent with the hypothesis

(∥∥, \overset{h}{true} (t)) < 1

. Remark In , synchronization of chaos systems was discussed with time‐delayed feedback controller u = k 1 e ( t ) + k 2 e ( t − τ ). In , synchronization conditions of complex networks with time‐varying delayed were obtained, τ ( t ) is the time‐varying delayed satisfying that

\overset{τ}{true} (t) \leq \overset{_{⌢}}{τ} < 1

, and the authors have concentrated on studying the presetting time‐varying delayed function in numerical examples yet.…”

Section: Adaptive Projective Schronizationmentioning

confidence: 99%

“…In [14][15][16][17][18][19], synchronization of chaos systems was discussed with time-delayed feedback controller u D k 1 e.t/ C k 2 e.t /. In [20][21][22][23][24], synchronization conditions of complex networks with time-varying delayed were obtained, .t/ is the time-varying delayed satisfying that P .t/ Ä…”

Section: Remarkmentioning

confidence: 99%

“…a > 0 represents the saving amount, b > 0 represents the cost per investment, and c > 0 represents the elasticity of demand of commercial markets. Then, the dynamical behavior of the finance system was investigated [2][3][4][5][6], and variety of method and techniques has been proposed for the control and synchronization of the chaotic finance system such as linear and nonlinear feedback synchronization [7,8], adaptive synchronization [9,10], observer-based control method [11,12], robust control [13], and impulsive control [14].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Chaos projective synchronization of the chaotic finance system with parameter switching perturbation and input time‐varying delay

Xu¹,

Xie²,

Wang

et al. 2014

Math Methods in App Sciences

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Communicated by B. HarrachThis paper discusses some basic dynamical properties of the chaotic finance system with parameter switching perturbation, and investigates chaos projective synchronization of the chaotic finance system with the time-varying delayed feedback controller, which are not fully considered in the existing research. Different from the previous methods, in this paper, the delayed feedback controller is not only time-varying, but also the time-varying delay is adaptive. Finally, an illustrate example is provided to show the effectiveness of this method.

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“…Proof See Appendix A. Remark Obviously,

(∥∥, \overset{h}{true} (t)) = (∥∥, \frac{h (t) x^{T} e}{((), (∥∥, h (t) x^{T} e) + γ)}) \leq τ < 1

. If γ = 0, then

(∥∥, \frac{h (t) x^{T} e}{((), (∥∥, h (t) x^{T} e) + γ)}) = 1

, it is not consistent with the hypothesis

(∥∥, \overset{h}{true} (t)) < 1

\overset{τ}{true} (t) \leq \overset{_{⌢}}{τ} < 1

, and the authors have concentrated on studying the presetting time‐varying delayed function in numerical examples yet.…”

Section: Adaptive Projective Schronizationmentioning

confidence: 99%

Section: Remarkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Chaos projective synchronization of the chaotic finance system with parameter switching perturbation and input time‐varying delay

Xu¹,

Xie²,

Wang

et al. 2014

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

“…Thus the central question becomes: how do neurons accurately respond to the signals of interest from a complex environment? Several mechanisms have been proposed to answer this question [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. One of the most interesting and counterintuitive mechanism is the stochastic resonance (SR) [20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Effect of initial phase diversity on signal detection in excitable systems

Liang

Liu

2016

Sci. China Technol. Sci.

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Undoubtedly, the sensory organs of biological systems have been evolved to accurately detect and locate the external stimuli, even if they are very weak. However, the mechanism underlying this ability is still not fully understood. Previously, it had been shown that stochastic resonance may be a good candidate to explain this ability, by which the response of a system to an external signal is amplified by the presence of noise. Recently, it is pointed out that the initial phase diversity in external signals can be also served as a simple and feasible mechanism for weak signal detection or amplification in excitable neurons. We here make a brief review on this progress. We will show that there are two kinds of effects of initial phase diversity: one is the phase disorder, i.e., the initial phases are different and static, and the other is the phase noise, i.e., the initial phases are time-varying like noise. Both cases show that initial phase diversity in subthreshold periodic signals can indeed play a constructive role in the emergence of sustained spiking activity. As initial phase diversity can mimic different arrival times from source signal to sensory organs, these findings may provide a cue for understanding the hunting behaviors of some biological systems.stochastic resonance, excitable neuron, phase noise, subthreshold signal Citation:Liang X M, Liu Z H. Effect of initial phase diversity on signal detection in excitable systems.

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“…Toral et al [11] have studied the existence of a system size coherence resonance effect in the coupled FHN models. Stochastic resonance (SR) in a FHN system with time-delayed feedback has been analyzed by Wu and Zhu [12]. They have revealed that SR of the system is a nonmonotonic function of the noise intensity and the signal period and variation of the time-delayed feedback can induce periodic SR in the system.…”

Section: Introductionmentioning

confidence: 99%

Effect of correlation in FitzHugh–Nagumo model with non-Gaussian noise and multiplicative signal

Ning

2015

Indian J Phys

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The effect of correlation in FitzHugh-Nagumo neural model induced by non-Gaussian noise and multiplicative signal is studied. Based on the corresponding Fokker-Planck equation, the explicit expressions of the stationary probability distribution function, the mean first passage time and signal-to-noise ratio are obtained, respectively. By analyzing the influence of different parameters, we observe that the system undergoes a succession of phase transition-like phenomena as correlation strength k, correlation time s and multiplicative noise intensity D are increased. And the mean first passage time exhibits a maximum, which identifies the noise-enhanced stability effect when correlation strength k \ 0. Furthermore, inhibition phenomenon and double stochastic resonance occur in FitzHugh-Nagumo neural model under different values of system parameters.

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Stochastic resonance in FitzHugh–Nagumo system with time-delayed feedback

Cited by 51 publications

References 49 publications

Chaos projective synchronization of the chaotic finance system with parameter switching perturbation and input time‐varying delay

Chaos projective synchronization of the chaotic finance system with parameter switching perturbation and input time‐varying delay

Effect of initial phase diversity on signal detection in excitable systems

Effect of correlation in FitzHugh–Nagumo model with non-Gaussian noise and multiplicative signal

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