scholarly journals Complex Behaviors of Epidemic Model with Nonlinear Rewiring Rate

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Ding Fang ◽  
Yongxin Zhang ◽  
Wendi Wang
Keyword(s):  
Hopf Bifurcation ◽  
Numerical Simulations ◽  
Bifurcation Analysis ◽  
Epidemic Model ◽  
Multiple Equilibria ◽  
Homoclinic Bifurcation ◽  
Propagation Model ◽  
Bifurcation Curve ◽  
Saddle Node Bifurcation ◽  
Saddle Node

An SIS propagation model with the nonlinear rewiring rate on an adaptive network is considered. It is found by bifurcation analysis that the model has the complex behaviors which include the transcritical bifurcation, saddle-node bifurcation, Hopf bifurcation, and Bogdanov–Takens bifurcation. Especially, a bifurcation curve with “S” shape emerges due to the nonlinear rewiring rate, which leads to multiple equilibria and twice saddle-node bifurcations. Numerical simulations show that the model admits a homoclinic bifurcation and a saddle-node bifurcation of the limit cycle.

Bifurcation analysis method of nonlinear traffic phenomena

2015 ◽  
Vol 26 (10) ◽  
pp. 1550111 ◽  
Author(s):  
Wenhuan Ai ◽  
Zhongke Shi ◽  
Dawei Liu
Keyword(s):  
Hopf Bifurcation ◽  
Traffic Flow ◽  
Bifurcation Analysis ◽  
Phase Plane ◽  
Flow Model ◽  
Analysis Method ◽  
Equilibrium Solutions ◽  
Saddle Node Bifurcation ◽  
Traffic Flow Model ◽  
Saddle Node

A new bifurcation analysis method for analyzing and predicting the complex nonlinear traffic phenomena based on the macroscopic traffic flow model is presented in this paper. This method makes use of variable substitution to transform a traditional traffic flow model into a new model which is suitable for the stability analysis. Although the substitution seems to be simple, it can extend the range of the variable to infinity and build a relationship between the traffic congestion and the unstable system in the phase plane. So the problem of traffic flow could be converted into that of system stability. The analysis identifies the types and stabilities of the equilibrium solutions of the new model and gives the overall distribution structure of the nearby equilibrium solutions in the phase plane. Then we deduce the existence conditions of the models Hopf bifurcation and saddle-node bifurcation and find some bifurcations such as Hopf bifurcation, saddle-node bifurcation, Limit Point bifurcation of cycles and Bogdanov–Takens bifurcation. Furthermore, the Hopf bifurcation and saddle-node bifurcation are selected as the starting point of density temporal evolution and it will be helpful for improving our understanding of stop-and-go wave and local cluster effects observed in the free-way traffic.

Bifurcation Analysis of the Wound Rotor Induction Motor

2015 ◽  
Vol 25 (12) ◽  
pp. 1550163 ◽  
Author(s):  
R. Salas-Cabrera ◽  
A. Hernandez-Colin ◽  
J. Roman-Flores ◽  
N. Salas-Cabrera
Keyword(s):  
Hopf Bifurcation ◽  
Induction Motor ◽  
Bifurcation Analysis ◽  
Open Loop ◽  
Experimental Results ◽  
Saddle Node Bifurcation ◽  
Saddle Node ◽  
Bifurcation Phenomena ◽  
Three Phase ◽  
The Individual

This work deals with the bifurcation phenomena that occur during the open-loop operation of a single-fed three-phase wound rotor induction motor. This paper demonstrates the occurrence of saddle-node bifurcation, hysteresis, supercritical saddle-node bifurcation, cusp and Hopf bifurcation during the individual operation of this electromechanical system. Some experimental results associated with the bifurcation phenomena are presented.

APPLICATION OF A TWO-DIMENSIONAL HINDMARSH–ROSE TYPE MODEL FOR BIFURCATION ANALYSIS

2013 ◽  
Vol 23 (03) ◽  
pp. 1350055 ◽  
Author(s):  
SHYAN-SHIOU CHEN ◽  
CHANG-YUAN CHENG ◽  
YI-RU LIN
Keyword(s):  
Hopf Bifurcation ◽  
Bifurcation Analysis ◽  
Sufficient Conditions ◽  
Type Model ◽  
Two Dimensional ◽  
Saddle Node Bifurcation ◽  
Trapping Region ◽  
Saddle Node ◽  
The Stability ◽  
Two Equilibria

In this study, we examine the bifurcation scenarios of a two-dimensional Hindmarsh–Rose type model [Tsuji et al., 2007] with four parameters and simulate some resemblances of neurophysiological features for this model using spike-and-reset conditions. We present possible classifications based on the results of the following assessments: (1) the number and stability of the equilibria are analyzed in detail using a table to demonstrate the matter in which the stability of the equilibrium changes and to determine which two equilibria collapse through the saddle-node bifurcation; (2) the sufficient conditions for an Andronov–Hopf bifurcation and a saddle-node bifurcation are mathematically confirmed; and (3) we elaborately evaluate the sufficient conditions for the Bogdanov–Takens (BT) and Bautin bifurcations. Several numerical simulations for these conditions are also presented. In particular, two types of bistable behaviors are numerically demonstrated: the BT and Bautin bifurcations. Notably, all of the bifurcation curves in the domain of the remaining parameters are similar when the time scale is large. Additionally, to show the potential for a limit cycle, the existence of a trapping region is demonstrated. These results present a variety of diverse behaviors for this model. The results of this study will be helpful in assessing suitable parameters for fitting the resemblances of experimental observations.

scholarly journals Stability and Hopf Bifurcation Analysis of a Fractional-Order Epidemic Model with Time Delay

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Zhen Wang ◽  
Xinhe Wang
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Numerical Simulations ◽  
Equilibrium Point ◽  
Fractional Order ◽  
Bifurcation Analysis ◽  
Epidemic Model ◽  
Bifurcation Parameter ◽  
Theoretical Results ◽  
Disease Free

A fractional-order epidemic model with time delay is considered. Firstly, stability of the disease-free equilibrium point and endemic equilibrium point is studied. Then, by choosing the time delay as a bifurcation parameter, the existence of Hopf bifurcation is studied. Finally, numerical simulations are given to illustrate the effectiveness and feasibility of theoretical results.

Bifurcation Analysis of an SIV Epidemic Model with the Saturated Incidence Rate

2014 ◽  
Vol 24 (05) ◽  
pp. 1450060 ◽  
Author(s):  
Yakui Xue ◽  
Xiaoming Tang ◽  
Xinpeng Yuan
Keyword(s):  
Population Dynamics ◽  
Hopf Bifurcation ◽  
Numerical Simulations ◽  
Incidence Rate ◽  
Bifurcation Analysis ◽  
Epidemic Model ◽  
Vaccination Strategy ◽  
Saturated Incidence Rate ◽  
Saturated Incidence

In this paper, an SIV epidemic model with the saturated incidence rate is investigated, considering the factors of population dynamics such as the constant recruitment of population, the natural morality and vaccination strategy. By carrying out the bifurcation analysis of the model, it is shown that numerous kinds of bifurcation occur for the model, such as Hopf bifurcation and Bogdanov–Takens bifurcation. The main results are illustrated by numerical simulations.

scholarly journals Numerical Study of One Prey-Two Predator Model Considering Food Addition and Anti-Predator Defense

2021 ◽  
Vol 328 ◽  
pp. 06003
Author(s):  
Dian Savitri
Keyword(s):  
Mathematical Model ◽  
Hopf Bifurcation ◽  
Numerical Simulations ◽  
Numerical Study ◽  
Saddle Node Bifurcation ◽  
Predator Defense ◽  
Saddle Node ◽  
System Solution ◽  
Predator Model ◽  
Prey Populations

This article examines the interaction between prey populations, juvenile predators, and adult predators. A mathematical model that considers adding food and anti-predators was developed. The equilibria of the existing system are that the system has four equilibria points with conditions suitable for the locale. Numerical simulations were carried out to describe the dynamics of the system solution. Based on numerical simulations, the varying of parameter causes changes in the extinction of prey or survival of prey populations, juvenile predators, and adult predators. Addfood parameters (A) encourae Hopf Bifurcation and Saddle-node bifurcation Numerical continuity results show that Hopf bifurcation occurs when the parameter value A = 1.00162435 and when the parameter value A = 2.435303 Saddle-node bifurcation occurs.

COHERENCE RESONANCE–INDUCED STOCHASTIC NEURAL FIRING AT A SADDLE-NODE BIFURCATION

2011 ◽  
Vol 25 (29) ◽  
pp. 3977-3986 ◽  
Author(s):  
HUAGUANG GU ◽  
HUIMIN ZHANG ◽  
CHUNLING WEI ◽  
MINGHAO YANG ◽  
ZHIQIANG LIU ◽  
...  
Keyword(s):  
Hopf Bifurcation ◽  
Bifurcation Point ◽  
Firing Pattern ◽  
Neuronal System ◽  
Neural Firing ◽  
Coherence Resonance ◽  
Saddle Node Bifurcation ◽  
Hopf Bifurcation Point ◽  
Firing Patterns ◽  
Saddle Node

Coherence resonance at a saddle-node bifurcation point and the corresponding stochastic firing patterns are simulated in a theoretical neuronal model. The characteristics of noise-induced neural firing pattern, such as exponential decay in histogram of interspike interval (ISI) series, independence and stochasticity within ISI series are identified. Firing pattern similar to the simulated results was discovered in biological experiment on a neural pacemaker. The difference between this firing and integer multiple firing generated at a Hopf bifurcation point is also given. The results not only revealed the stochastic dynamics near a saddle-node bifurcation, but also gave practical approaches to identify the saddle-node bifurcation and to distinguish it from the Hopf bifurcation in neuronal system. In addition, many previously observed firing patterns can be attribute to stochastic firing pattern near such a saddle-node bifurcation.

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