scholarly journals Reinterpreting the Origin of Bifurcation and Chaos by Urbanization Dynamics

Chaos Theory ◽  
2018 ◽  
Author(s):  
Yanguang Chen
Keyword(s):  
Bifurcation And Chaos

scholarly journals Bifurcation and chaos analysis for a discrete ecological developmental systems

2021 ◽  
Author(s):  
Xiao-Wei Jiang ◽  
Chaoyang Chen ◽  
Xian-He Zhang ◽  
Ming Chi ◽  
Huaicheng Yan
Keyword(s):  
Developmental Systems ◽  
Bifurcation And Chaos ◽  
Chaos Analysis

Bifurcation and Chaos of a 4-Side Simply Supported Rectangular Thin Electro-Magneto-Elastic Plate in Many Fields

2010 ◽  
Vol 97-101 ◽  
pp. 442-448
Author(s):  
Wei Guo Zhu ◽  
Xiang Zhong Bai
Keyword(s):  
Elastic Plate ◽  
Transverse Magnetic ◽  
Temperature Fields ◽  
Bifurcation And Chaos ◽  
Simply Supported ◽  
Runge Kutta Method ◽  
Displacement Wave ◽  
Nonlinear Temperature ◽  
Electro Magnetic ◽  
Chaos Motion

The problem of bifurcation and chaos in a 4-side simply supported rectangular thin electro-magneto-elastic plate in electro-magnetic, mechanical and temperature fields is studied. Based on the basic nonlinear electro-magneto-elastic motion equations for a rectangular thin plate and expressions of electromagnetic forces, vibration equations are derived for the mechanical loading in a nonlinear temperature field and a steady transverse magnetic field. By using Melnikov function method, the criteria are obtained for chaos motion to exist as demonstrated by the Smale horseshoe mapping. The vibration equations are solved numerically by using a fourth-order Runge-Kutta method. Its bifurcation diagram, Lyapunov exponents diagram, displacement wave diagram, phase diagram and Poincare section diagram are obtained for some examples. The characteristics of the vibration system are analyzed, and the roles of parameters on the systems are discussed separately as well, such as electromagnetic field intensity, temperature and mechanical force.

Stability, bifurcation and chaos control of a discretized Leslie prey-predator model

2021 ◽  
Vol 152 ◽  
pp. 111345
Author(s):  
S. Akhtar ◽  
R. Ahmed ◽  
M. Batool ◽  
Nehad Ali Shah ◽  
Jae Dong Chung
Keyword(s):  
Chaos Control ◽  
Bifurcation And Chaos ◽  
Predator Model

scholarly journals Stability, Bifurcation and Chaos Analysis of Vector-Borne Disease Model with Application to Rift Valley Fever

PLoS ONE ◽  
2014 ◽  
Vol 9 (10) ◽  
pp. e108172 ◽  
Author(s):  
Sansao A. Pedro ◽  
Shirley Abelman ◽  
Frank T. Ndjomatchoua ◽  
Rosemary Sang ◽  
Henri E. Z. Tonnang
Keyword(s):  
Rift Valley ◽  
Rift Valley Fever ◽  
Disease Model ◽  
Bifurcation And Chaos ◽  
Valley Fever ◽  
Chaos Analysis ◽  
Vector Borne Disease ◽  
Vector Borne

BIFURCATION AND CHAOS IN A DISCRETE PREDATOR–PREY MODEL WITH HOLLING TYPE-III FUNCTIONAL RESPONSE AND HARVESTING EFFECT

2021 ◽  
pp. 1-28
Author(s):  
ANURAJ SINGH ◽  
PREETI DEOLIA
Keyword(s):  
Functional Response ◽  
Sufficient Conditions ◽  
Flip Bifurcation ◽  
Bifurcation Structure ◽  
Bifurcation And Chaos ◽  
Predator Prey ◽  
Type Iii ◽  
Predator Prey Model ◽  
Prey Model ◽  
Wide Range

In this paper, we study a discrete-time predator–prey model with Holling type-III functional response and harvesting in both species. A detailed bifurcation analysis, depending on some parameter, reveals a rich bifurcation structure, including transcritical bifurcation, flip bifurcation and Neimark–Sacker bifurcation. However, some sufficient conditions to guarantee the global asymptotic stability of the trivial fixed point and unique positive fixed points are also given. The existence of chaos in the sense of Li–Yorke has been established for the discrete system. The extensive numerical simulations are given to support the analytical findings. The system exhibits flip bifurcation and Neimark–Sacker bifurcation followed by wide range of dense chaos. Further, the chaos occurred in the system can be controlled by choosing suitable value of prey harvesting.

scholarly journals Analysis of Bifurcation and Chaos of the Size-dependent Micro–plate Considering Damage

2019 ◽  
Vol 8 (1) ◽  
pp. 461-469 ◽  
Author(s):  
Xiumei Wang ◽  
Jihai Yuan ◽  
Haorui Zhai
Keyword(s):  
Internal State ◽  
Couple Stress Theory ◽  
Damage Model ◽  
Modified Couple Stress Theory ◽  
Damage Effect ◽  
Bifurcation And Chaos ◽  
Stress Theory ◽  
Size Dependent ◽  
Material Length Scale ◽  
Plate System

Abstract In this research, nonlinear dynamics and characteristics of a micro–plate system under electrostatic forces on both sides are studied. A novel model, which takes micro-scale effect and damage effect into account, is established on the basis of the Talreja’s tensor valued internal state damage model and modified couple stress theory. According to Hamilton principle, the dynamic governing equations of the size-dependent micro–plate are derived by variational method and solved via Galerkin method and the fourth order Runge-Kutta method. The effects of damage variable and material length scale parameter on bifurcation and chaos of the micro–plate system are presented with numerical simulations using the bifurcation diagram, Poincare map. Results provide a theoretical basis for the design of dynamic stability of electrically actuated micro- structures.

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