Bifurcation analysis of an extended macro model considering time delay and anticipation effect

2021 ◽  
pp. 126434
Author(s):  
Hao Lyu ◽  
Rongjun Cheng ◽  
Hongxia Ge
Keyword(s):  
Time Delay ◽  
Bifurcation Analysis ◽  
Macro Model ◽  
Anticipation Effect

scholarly journals Spatiotemporal Patterns Formed by a Discrete Nutrient-Phytoplankton Model with Time Delay

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Feifan Zhang ◽  
Wenjiao Zhou ◽  
Lei Yao ◽  
Xuanwen Wu ◽  
Huayong Zhang
Keyword(s):  
Steady State ◽  
Time Delay ◽  
Numerical Simulations ◽  
Functional Response ◽  
Bifurcation Analysis ◽  
Discrete Model ◽  
Continuous Model ◽  
Spatiotemporal Patterns ◽  
Homogeneous Steady State ◽  
Simulation Results

In this research, a continuous nutrient-phytoplankton model with time delay and Michaelis–Menten functional response is discretized to a spatiotemporal discrete model. Around the homogeneous steady state of the discrete model, Neimark–Sacker bifurcation and Turing bifurcation analysis are investigated. Based on the bifurcation analysis, numerical simulations are carried out on the formation of spatiotemporal patterns. Simulation results show that the diffusion of phytoplankton and nutrients can induce the formation of Turing-like patterns, while time delay can also induce the formation of cloud-like pattern by Neimark–Sacker bifurcation. Compared with the results generated by the continuous model, more types of patterns are obtained and are compared with real observed patterns.

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

BIFURCATION ANALYSIS OF A DETRITUS-BASED ECOSYSTEM WITH TIME DELAY

2000 ◽  
Vol 08 (03) ◽  
pp. 255-261 ◽  
Author(s):  
DEBASIS MUKHERJEE ◽  
SANTANU RAY ◽  
DILIP KUMAR SINHA
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Bifurcation Analysis ◽  
Local Stability ◽  
Mangrove Ecosystem ◽  
Stability Criteria ◽  
Delay Effect

This article concentrates on the study of delay effect of a mangrove ecosystem of detritus, detritivores and predator of detritivores. Local stability criteria are derived in the absence of delays. Conditions are found out for which the system undergoes a Hopf bifurcation. Further conditions are derived for which there can be no change in stability.

scholarly journals Bifurcation analysis of a model for network worm propagation with time delay

2010 ◽  
Vol 52 (3-4) ◽  
pp. 435-447 ◽  
Author(s):  
Shaojie Wang ◽  
Qiming Liu ◽  
Xinfeng Yu ◽  
Yi Ma
Keyword(s):  
Time Delay ◽  
Bifurcation Analysis ◽  
Worm Propagation

scholarly journals Chaos and Hopf Bifurcation Analysis of the Delayed Local Lengyel-Epstein System

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Qingsong Liu ◽  
Yiping Lin ◽  
Jingnan Cao ◽  
Jinde Cao
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Numerical Simulations ◽  
Bifurcation Analysis ◽  
Center Manifold ◽  
Local Reaction ◽  
Reaction Diffusion ◽  
Critical Value ◽  
Hopf Bifurcations ◽  
The Stability

The local reaction-diffusion Lengyel-Epstein system with delay is investigated. By choosingτas bifurcating parameter, we show that Hopf bifurcations occur when time delay crosses a critical value. Moreover, we derive the equation describing the flow on the center manifold; then we give the formula for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions. Finally, numerical simulations are performed to support the analytical results and the chaotic behaviors are observed.

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