Dynamical behavior of a Lotka–Volterra competition system in open advective environments

2021 ◽  
Author(s):  
Xiao Yan ◽  
Hua Nie ◽  
Yanling Li ◽  
Jianhua Wu
Keyword(s):  
Dynamical Behavior ◽  
Competition System

Existence and Stability of Stationary States of a Reaction–Diffusion-Advection Model for Two Competing Species

2020 ◽  
Vol 30 (05) ◽  
pp. 2050065
Author(s):  
Li Ma ◽  
De Tang
Keyword(s):  
Dynamical Behavior ◽  
Reaction Diffusion ◽  
Similar Species ◽  
Resident Species ◽  
Competition System ◽  
Special Cases ◽  
Existence And Stability ◽  
Maximal Growth Rate ◽  
Steady State Solutions ◽  
Monotone Dynamical Systems

It is well known that the research of two species in the Lotka–Volterra competition system could create very interesting dynamics. In our paper, we investigate the global dynamical behavior of a classic Lotka–Volterra competition system by studying the steady states and corresponding stability by mainly employing the methods of monotone dynamical systems theory, Lyapunov–Schmidt reduction and spectral theory and so on. It illustrates that the dynamical behavior substantially relies on certain variable of the maximal growth rate. Furthermore, we obtain that one of the semi-trivial steady state solutions is a global attractor in some special cases. In biology, these results show that both of the species do not coexist and the mutant forces the extinction of resident species under some condition for two similar species system.

Dynamical behavior of a nonlinear rotorcraft model

1989 ◽  
Author(s):  
GEORGE FLOWERS ◽  
BENSONH. TONGUE
Keyword(s):  
Dynamical Behavior

Probing the dynamical behavior in glass transition of PVPh-PEO blend

2021 ◽  
Vol 554 ◽  
pp. 120561
Author(s):  
Yong-jin Peng ◽  
He-Huang ◽  
Chang-jun Wang ◽  
Zhong-fu Zuo ◽  
Xue-zheng Liu
Keyword(s):  
Glass Transition ◽  
Dynamical Behavior

scholarly journals A Characterization of the Dynamics of Schröder’s Method for Polynomials with Two Roots

2021 ◽  
Vol 5 (1) ◽  
pp. 25
Author(s):  
Víctor Galilea ◽  
José M. Gutiérrez
Keyword(s):  
Nonlinear Equations ◽  
Complex Plane ◽  
Iterative Process ◽  
Dynamical Behavior ◽  
Basins Of Attraction ◽  
Schröder’S Method

The purpose of this work is to give a first approach to the dynamical behavior of Schröder’s method, a well-known iterative process for solving nonlinear equations. In this context, we consider equations defined in the complex plane. By using topological conjugations, we characterize the basins of attraction of Schröder’s method applied to polynomials with two roots and different multiplicities. Actually, we show that these basins are half-planes or circles, depending on the multiplicities of the roots. We conclude our study with a graphical gallery that allow us to compare the basins of attraction of Newton’s and Schröder’s method applied to some given polynomials.

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