Stability switches, Hopf bifurcation and chaos of a neuron model with delay-dependent parameters

2006 ◽  
Vol 354 (1-2) ◽  
pp. 126-136 ◽  
Author(s):  
X. Xu ◽  
H.Y. Hu ◽  
H.L. Wang
Keyword(s):  
Hopf Bifurcation ◽  
Neuron Model ◽  
Stability Switches ◽  
Bifurcation And Chaos ◽  
Delay Dependent

scholarly journals Hopf bifurcation and chaos in a single inertial neuron model with time delay

2004 ◽  
Vol 41 (3) ◽  
pp. 337-343 ◽  
Author(s):  
Chunguang Li ◽  
Guangrong Chen ◽  
Xiaofeng Liao ◽  
Juebang Yu
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Neuron Model ◽  
Bifurcation And Chaos

scholarly journals Stability Switches and Hopf Bifurcation in a Kaleckian Model of Business Cycle

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Luca Vincenzo Ballestra ◽  
Luca Guerrini ◽  
Graziella Pacelli
Keyword(s):  
Hopf Bifurcation ◽  
Business Cycle ◽  
Transcendental Equation ◽  
Type Model ◽  
Stability Switches ◽  
Normal Form Theory ◽  
Center Manifold Theorem ◽  
Form Theory ◽  
Delay Differential ◽  
Delay Dependent

This paper considers a Kaleckian type model of business cycle based on a nonlinear delay differential equation, whose associated characteristic equation is a transcendental equation with delay dependent coefficients. Using the conventional analysis introduced by Beretta and Kuang (2002), we show that the unique equilibrium can be destabilized through a Hopf bifurcation and stability switches may occur. Then some properties of Hopf bifurcation such as direction, stability, and period are determined by the normal form theory and the center manifold theorem.

scholarly journals Global Stability and Hopf-bifurcation Analysis of Biological Systems using Delayed Extended Rosenzweig-MacArthur Model

2018 ◽  
Vol 12 (2) ◽  
pp. 171
Author(s):  
Enobong E. Joshua ◽  
Cec Ekemini T. Akpan
Keyword(s):  
Experimental Data ◽  
Population Dynamics ◽  
Hopf Bifurcation ◽  
Asymptotic Stability ◽  
Asymptotically Stable ◽  
Stability Switches ◽  
Large Delay ◽  
Local Hopf Bifurcation ◽  
Delay Margin ◽  
Theoretical Results

This paper investigates the global asymptotic stability of a Delayed Extended Rosenzweig-MacArthur Model via Lyapunov-Krasovskii functionals. Frequency sweeping technique ensures stability switches as the delay parameter increases and passes the critical bifurcating threshold.The model exhibits a local Hopf-bifurcation from asymptotically stable oscillatory behaviors to unstable strange chaotic behaviors dependent of the delay parameter values.Hyper-chaotic fluctuations were observed for large delay values far away from the critical delay margin. Numerical simulations of experimental data obtained via non-dimensionalization have shown the applications of theoretical results in ecological population dynamics.

Hopf bifurcation and chaos in macroeconomic models with policy lag

2005 ◽  
Vol 25 (1) ◽  
pp. 91-108 ◽  
Author(s):  
Xiaofeng Liao ◽  
Chuandong Li ◽  
Shangbo Zhou
Keyword(s):  
Hopf Bifurcation ◽  
Bifurcation And Chaos ◽  
Macroeconomic Models

scholarly journals Hopf Bifurcation and Chaos of a Delayed Finance System

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-18 ◽  
Author(s):  
Xuebing Zhang ◽  
Honglan Zhu
Keyword(s):  
Numerical Simulation ◽  
Hopf Bifurcation ◽  
Center Manifold ◽  
Chaotic State ◽  
Bifurcation And Chaos ◽  
Finance System ◽  
Center Manifold Theorem ◽  
Normal Form Method ◽  
Simulation Results ◽  
The Stability

In this paper, a finance system with delay is considered. By analyzing the corresponding characteristic equations, the local stability of equilibrium is established. The existence of Hopf bifurcations at the equilibrium is also discussed. Furthermore, formulas for determining the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by applying the normal form method and center manifold theorem. Finally, numerical simulation results are presented to validate the theoretical analysis. Numerical simulation results show that delay can lead a stable system into a chaotic state.

Stability Switches of a Class of Fractional-Delay Systems With Delay-Dependent Coefficients

2018 ◽  
Vol 13 (11) ◽  
Author(s):  
Xinghu Teng ◽  
Zaihua Wang
Keyword(s):  
Time Delay ◽  
Delay Systems ◽  
Jacobian Determinant ◽  
Stability Switches ◽  
Characteristic Roots ◽  
Fractional Delay ◽  
Analysis Of Stability ◽  
The Stability ◽  
Key Steps ◽  
Delay Dependent

Stability of a dynamical system may change from stable to unstable or vice versa, with the change of some parameter of the system. This is the phenomenon of stability switches, and it has been investigated intensively in the literature for conventional time-delay systems. This paper studies the stability switches of a class of fractional-delay systems whose coefficients depend on the time delay. Two simple formulas in closed-form have been established for determining the crossing direction of the characteristic roots at a given critical point, which is one of the two key steps in the analysis of stability switches. The formulas are expressed in terms of the Jacobian determinant of two auxiliary real-valued functions that are derived directly from the characteristic function, and thus, can be easily implemented. Two examples are given to illustrate the main results and to show an important difference between the fractional-delay systems with delay-dependent coefficients and the ones with delay-free coefficients from the viewpoint of stability switches.

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