On Qualitative Analysis of Lattice Dynamical System of Two- and Three-Dimensional Biopixels Array: Bifurcations and Transition to “Chaos”

2021 ◽  
pp. 23-43
Author(s):  
Oleksandr Nakonechnyi ◽  
Vasyl Martsenyuk ◽  
Mikolaj Karpinski ◽  
Aleksandra Klos-Witkowska
Keyword(s):  
Dynamical System ◽  
Qualitative Analysis ◽  
Three Dimensional ◽  
Transition To Chaos ◽  
Lattice Dynamical System

scholarly journals Upper semicontinuity of the attractor for lattice dynamical systems of partly dissipative reaction diffusion systems

2005 ◽  
Vol 2005 (3) ◽  
pp. 273-288 ◽  
Author(s):  
Ahmed Y. Abdallah
Keyword(s):  
Dynamical System ◽  
Hilbert Space ◽  
Upper Semicontinuity ◽  
Reaction Diffusion ◽  
Dimensional Lattice ◽  
Reaction Diffusion Systems ◽  
Infinite Dimensional ◽  
Diffusion Systems ◽  
Lattice Dynamical System ◽  
Lattice Dynamical Systems

We investigate the existence of a global attractor and its upper semicontinuity for the infinite-dimensional lattice dynamical system of a partly dissipative reaction diffusion system in the Hilbert spacel2×l2. Such a system is similar to the discretized FitzHugh-Nagumo system in neurobiology, which is an adequate justification for its study.

A Stochastic Hierarchical Population System: Excitement, Extinction and Transition to Chaos

2021 ◽  
Vol 31 (14) ◽  
Author(s):  
Irina Bashkirtseva ◽  
Tatyana Perevalova ◽  
Lev Ryashko
Keyword(s):  
Mathematical Modeling ◽  
Food Chain ◽  
Analytical Method ◽  
Three Dimensional ◽  
Biological Parameters ◽  
Top Predator ◽  
Population System ◽  
Modeling And Analysis ◽  
Transition To Chaos ◽  
Random Fluctuations

A problem of the mathematical modeling and analysis of noise-induced transformations of complex oscillatory regimes in hierarchical population systems is considered. As a key example, we use a three-dimensional food chain dynamical model of the interacting prey, predator, and top predator. We perform a comparative study of the impacts of random fluctuations on three key biological parameters of prey growth, predator mortality, and the top predator growth. A detailed investigation of the stochastic excitement, noise-induced transition from order to chaos, and various scenarios of extinction is carried out. Constructive abilities of the semi-analytical method of confidence domains in the analysis of the noise-induced extinction are demonstrated.

DYNAMICS AT INFINITY OF A CUBIC CHUA'S SYSTEM

2011 ◽  
Vol 21 (01) ◽  
pp. 333-340 ◽  
Author(s):  
MARCELO MESSIAS
Keyword(s):  
Dynamical System ◽  
Vector Field ◽  
Numerical Study ◽  
Three Dimensional ◽  
Polynomial Vector ◽  
Cubic Nonlinearity ◽  
Poincaré Compactification ◽  
Global Study ◽  
Dimensional Dynamical System ◽  
Parameter Values

We use the Poincaré compactification for a polynomial vector field in ℝ3 to study the dynamics near and at infinity of the classical Chua's system with a cubic nonlinearity. We give a complete description of the phase portrait of this system at infinity, which is identified with the sphere 𝕊2 in ℝ3 after compactification, and perform a numerical study on how the solutions reach infinity, depending on the parameter values. With this global study we intend to give a contribution in the understanding of this well known and extensively studied complex three-dimensional dynamical system.

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