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.

scholarly journals Dynamic properties of the coupled Oregonator model with delay

2013 ◽  
Vol 18 (3) ◽  
pp. 377-397
Author(s):  
Xiang Wu ◽  
Chunrui Zhang
Keyword(s):  
Hopf Bifurcation ◽  
Center Manifold ◽  
Dynamic Properties ◽  
Hopf Bifurcations ◽  
Center Manifold Reduction ◽  
Multiple Periodic Solutions ◽  
Normal Form Method ◽  
The Stability ◽  
Oregonator Model ◽  
Manifold Reduction

This work explores a coupled Oregonator model. By analyzing the associated characteristic equation, linear stability is investigated and Hopf bifurcations are demonstrated, as well as the stability and direction of the Hopf bifurcation are determined by employing the normal form method and the center manifold reduction. We also discussed the Z2 equivariant property and the existence of multiple periodic solutions. Numerical simulations are presented to illustrate the results in Section 5.

scholarly journals Stability and Hopf bifurcation analysis of fractional order nonlinear financial system with time delay

2021 ◽  
Author(s):  
SANTOSHI PANIGRAHI ◽  
Sunita Chand ◽  
S Balamuralitharan
Keyword(s):  
Numerical Simulation ◽  
Hopf Bifurcation ◽  
Time Delay ◽  
Fractional Order ◽  
Bifurcation Analysis ◽  
Laplace Transformation ◽  
Financial System ◽  
System With Time Delay

In this paper, we study a fractional order time delay for nonlinear financial system. By using Laplace transformation, stability and Hopf bifurcation analysis have been done for the model. Furthermore, numerical simulation has been carried out for better understanding of our results.

Time-delay-induced instabilities and Hopf bifurcation analysis in 2-neuron network model with reaction–diffusion term

2018 ◽  
Vol 313 ◽  
pp. 306-315 ◽  
Author(s):  
Swati Tyagi ◽  
Subit K Jain ◽  
Syed Abbas ◽  
Shahlar Meherrem ◽  
Rajendra K Ray
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Network Model ◽  
Bifurcation Analysis ◽  
Reaction Diffusion ◽  
Neuron Network ◽  
Diffusion Term

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.

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

scholarly journals Double Hopf Bifurcation in Microbubble Oscillators with Delay Coupling

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Jinbin Wang ◽  
Rui Zhang ◽  
Lifenq Ma
Keyword(s):  
Hopf Bifurcation ◽  
Center Manifold ◽  
Two Dimensional ◽  
Main Attention ◽  
Dimensional Parameter ◽  
Center Manifold Reduction ◽  
Double Hopf Bifurcation ◽  
Physical Phenomena ◽  
Manifold Reduction ◽  
Theoretical Results

Using center manifold reduction methodswe investigate the double Hopf bifurcation in the dynamics of microbubble with delay couplingwith main attention focused on nonresonant double Hopf bifurcation. We obtain the normal form of the system in the vicinity of the double Hopf point and classify the bifurcations in a two-dimensional parameter space near the critical point. Some numerical simulations support the applicability of the theoretical results. In particularwe give the explanation for some physical phenomena of the system using the obtained mathematical results.

Sign in / Sign up

Export Citation Format

Share Document