Two bifurcation routes to multiple chaotic coexistence in an inertial two-neural system with time delay

2018 ◽  
Vol 95 (2) ◽  
pp. 1549-1563 ◽  
Author(s):  
Shengwei Yao ◽  
Liwang Ding ◽  
Zigen Song ◽  
Jieqiong Xu
Keyword(s):  
Time Delay ◽  
Neural System ◽  
System With Time Delay

Dynamical behavior of simplified FitzHugh–Nagumo neural system with time delay driven by Lévy noise

2021 ◽  
pp. 2150240
Author(s):  
Weida Qiu ◽  
Yongfeng Guo ◽  
Xiuxian Yu
Keyword(s):  
Time Delay ◽  
First Passage Time ◽  
Dynamical Behavior ◽  
Passage Time ◽  
Neural System ◽  
The Other ◽  
Lévy Noise ◽  
First Passage ◽  
Levy Noise ◽  
System With Time Delay

In this paper, the dynamical behavior of the FitzHugh–Nagumo (FHN) neural system with time delay driven by Lévy noise is studied from two aspects: the mean first-passage time (MFPT) and the probability density function (PDF) of the first-passage time (FPT). Using the Janicki–Weron algorithm to generate the Lévy noise, and through the order-4 Runge–Kutta algorithm to simulate the FHN system response, the time that the system needs from one stable state to the other one is tracked in the process. Using the MATLAB software to simulate the process above 20,000 times and recording the PFTs, the PDF of the FPT and the MFPT is obtained. Finally, the effects of the Lévy noise and time-delay on the FPT are discussed. It is found that the increase of both time-delay feedback intensity and Lévy noise intensity can promote the transition of the particle from the resting state to the excited state. However, the two parameters produce the opposite effects in the other direction.

Stochastic Kinetics for a FitzHugh–Nagumo Neural System with Time Delay Driven by Non-Gaussian Noise and a Multiplicative Periodic Signal

2019 ◽  
Vol 18 (04) ◽  
pp. 1950027 ◽  
Author(s):  
Kang-Kang Wang ◽  
De-Cai Zong ◽  
Hui Ye ◽  
Ya-Jun Wang
Keyword(s):  
Time Delay ◽  
Probability Density ◽  
Gaussian Noise ◽  
Correlation Time ◽  
Neural System ◽  
Noise Correlation ◽  
Stable States ◽  
The Stability ◽  
Non Gaussian ◽  
System With Time Delay

In the present paper, the stability and the phenomena of stochastic resonance (SR) for a FitzHugh–Nagumo (FHN) system with time delay driven by a multiplicative non-Gaussian noise and an additive Gaussian white noise are investigated. By using the fast descent method, unified colored noise approximation and the two-state theory for the SR, the expressions for the stationary probability density function (SPDF) and the signal-to-noise ratio (SNR) are obtained. The research results show that the two noise intensities and time delay can always decrease the probability density at the two stable states and impair the stability of the neural system; while the noise correlation time [Formula: see text] can increase the probability density around both stable states and consolidate the stability of the neural system. Furthermore, the other noise correlation time [Formula: see text] can increase the probability at the resting state, but reduce that around the excited state. With respect to the SNR, it is discovered that the two noise strengths can both weaken the SR effect, while time delay [Formula: see text] and the departure parameter [Formula: see text] will always amplify the SR phenomenon. Moreover, the noise correlation time [Formula: see text] can motivate the SR effect, but not alter the peak value of the SNR. What’s most interesting is that the other noise correlation time [Formula: see text] can not only stimulate the SR phenomenon, but also results in the occurrence of two resonant peaks, whose heights are simultaneously improved because of the action of [Formula: see text].

FOLD–HOPF BIFURCATION ANALYSIS FOR A COUPLED FITZHUGH–NAGUMO NEURAL SYSTEM WITH TIME DELAY

2010 ◽  
Vol 20 (12) ◽  
pp. 3919-3934 ◽  
Author(s):  
BIN ZHEN ◽  
JIAN XU
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Bifurcation Analysis ◽  
Signal Transmission ◽  
Neural System ◽  
Center Manifold Reduction ◽  
Delayed Coupling ◽  
Normal Form Method ◽  
Manifold Reduction ◽  
System With Time Delay

A FitzHugh–Nagumo (FHN) model with delayed coupling is considered. For a critical case when the corresponding characteristic equation has a single zero root and a pair of purely imaginary roots, a complete bifurcation analysis is presented by employing the center manifold reduction and the normal form method. The Fold–Hopf bifurcation diagrams are provided to illustrate the correctness of our theoretical analysis. Whether almost periodic motion and bursting behavior occur in the FHN neural system with delayed coupling depends on the time delay in the signal transmission between the neurons.

The relaxation time of processes in a FitzHugh–Nagumo neural system with time delay

2011 ◽  
Vol 84 (2) ◽  
pp. 025009 ◽  
Author(s):  
Ailing Gong ◽  
Hua Wang ◽  
Chunhua Zeng
Keyword(s):  
Relaxation Time ◽  
Time Delay ◽  
Neural System ◽  
System With Time Delay

Design of Master's Position Controller for Bilateral Control System with Time Delay

2015 ◽  
Vol 135 (3) ◽  
pp. 268-275 ◽  
Author(s):  
Daisuke Yashiro ◽  
Tadashi Hieno ◽  
Kazuhiro Yubai ◽  
Satoshi Komada
Keyword(s):  
Control System ◽  
Time Delay ◽  
Bilateral Control ◽  
Position Controller ◽  
System With Time Delay

scholarly journals A time delay dynamical model for outbreak of 2019-nCoV and the parameter identification

2020 ◽  
Vol 28 (2) ◽  
pp. 243-250 ◽  
Author(s):  
Yu Chen ◽  
Jin Cheng ◽  
Yu Jiang ◽  
Keji Liu
Keyword(s):  
Dynamical System ◽  
Time Delay ◽  
Parameter Identification ◽  
Typical Feature ◽  
The Novel ◽  
Isolation Rate ◽  
High Isolation ◽  
The Government ◽  
System With Time Delay ◽  
Official Data

AbstractIn this paper, we propose a novel dynamical system with time delay to describe the outbreak of 2019-nCoV in China. One typical feature of this epidemic is that it can spread in the latent period, which can therefore be described by time delay process in the differential equations. The accumulated numbers of classified populations are employed as variables, which is consistent with the official data and facilitates the parameter identification. The numerical methods for the prediction of the outbreak of 2019-nCoV and parameter identification are provided, and the numerical results show that the novel dynamic system can well predict the outbreak trend so far. Based on the numerical simulations, we suggest that the transmission of individuals should be greatly controlled with high isolation rate by the government.

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