Steady State Bifurcation of Extended Fish-Kolmogorov System with Direchlet Boundary Condition

2019 ◽  
Vol 08 (06) ◽  
pp. 1114-1120
Author(s):  
英霞 王
Keyword(s):  
Boundary Condition ◽  
Steady State ◽  
Steady State Bifurcation ◽  
Kolmogorov System

scholarly journals Stability and Dynamical Analysis of a Biological System

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Xinhong Pan ◽  
Min Zhao ◽  
Yapei Wang ◽  
Hengguo Yu ◽  
Zengling Ma ◽  
...  
Keyword(s):  
Boundary Condition ◽  
Steady State ◽  
Local Stability ◽  
Allee Effect ◽  
Homogeneous Boundary Condition ◽  
Reaction Diffusion ◽  
Dynamical Analysis ◽  
Positive Equilibrium ◽  
Qualitative Properties ◽  
Steady State Bifurcation

This study considers the spatiotemporal dynamics of a reaction-diffusion phytoplankton-zooplankton system with a double Allee effect on prey under a homogeneous boundary condition. The qualitative properties are analyzed, including the local stability of all equilibria and the global asymptotic property of the unique positive equilibrium. We also discuss the Hopf bifurcation and the steady state bifurcation of the system. These results are expected to help understand the complexity of the Allee effect and the interaction between phytoplankton and zooplankton.

Rayleigh–Bénard convection and pattern formation in magnetohydrodynamics

1998 ◽  
Vol 60 (3) ◽  
pp. 529-539 ◽  
Author(s):  
RENU BAJAJ ◽  
S. K. MALIK
Keyword(s):  
Magnetic Field ◽  
Steady State ◽  
Thermal Instability ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
Steady State Bifurcation ◽  
The Stability ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard ◽  
The Magnetic Field

A nonlinear thermal instability in a layer of electrically conducting fluid in the presence of a magnetic field is discussed. Steady-state bifurcation results in the formation of patterns: rolls, squares and hexagons. The stability of various patterns is also investigated. It is found that in the absence of a magnetic field only rolls are stable, but when the magnetic field strength exceeds a certain finite value, squares and hexagons also become stable.

scholarly journals Deployment/Retrieval Modeling of Cable-Driven Parallel Robot

2010 ◽  
Vol 2010 ◽  
pp. 1-10 ◽  
Author(s):  
Q. J. Duan ◽  
J. L. Du ◽  
B. Y. Duan ◽  
A. F. Tang
Keyword(s):  
Mathematical Model ◽  
Boundary Condition ◽  
Steady State ◽  
Differential Equations ◽  
Parallel Robot ◽  
Lumped Mass ◽  
Dynamic Motion ◽  
Long Span ◽  
System A ◽  
Lumped Mass Method

A steady-state dynamic model of a cable in air is put forward by using some tensor relations. For the dynamic motion of a long-span Cable-Driven Parallel Robot (CDPR) system, a driven cable deployment and retrieval mathematical model of CDPR is developed by employing lumped mass method. The effects of cable mass are taken into account. The boundary condition of cable and initial values of equations is founded. The partial differential governing equation of each cable is thus transformed into a set of ordinary differential equations, which can be solved by adaptive Runge-Kutta algorithm. Simulation examples verify the effectiveness of the driven cable deployment and retrieval mathematical model of CDPR.

Steady-State Bifurcation for a Biological Depletion Model

2016 ◽  
Vol 26 (04) ◽  
pp. 1650066 ◽  
Author(s):  
Yan’e Wang ◽  
Jianhua Wu ◽  
Yunfeng Jia
Keyword(s):  
Steady State ◽  
Bifurcation Theory ◽  
Steady States ◽  
Two Dimensional ◽  
Implicit Function ◽  
Flux Boundary Condition ◽  
One Dimensional ◽  
Steady State Bifurcation ◽  
The Stability ◽  
Theoretical Results

A two-species biological depletion model in a bounded domain is investigated in which one species is a substrate and the other is an activator. Firstly, under the no-flux boundary condition, the asymptotic stability of constant steady-states is discussed. Secondly, by viewing the feed rate of the substrate as a parameter, the steady-state bifurcations from constant steady-states are analyzed both in one-dimensional kernel case and in two-dimensional kernel case. Finally, numerical simulations are presented to illustrate our theoretical results. The main tools adopted here include the stability theory, the bifurcation theory, the techniques of space decomposition and the implicit function theorem.

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