scholarly journals A non-linear discrete-time dynamical system related to epidemic SISI model

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Sobirjon K. Shoyimardonov
Keyword(s):  
Dynamical System ◽  
Discrete Time ◽  
Epidemic Model ◽  
Death Rate ◽  
Birth Rate ◽  
Evolution Operator ◽  
Crucial Point ◽  
Linear Evolution ◽  
Discrete Time Dynamical System ◽  
Non Linear

Abstract We consider SISI epidemic model with discrete-time. The crucial point of this model is that an individual can be infected twice. This non-linear evolution operator depends on seven parameters and we assume that the population size under consideration is constant, so death rate is the same with birth rate per unit time. Reducing to quadratic stochastic operator (QSO) we study the dynamical system of the SISI model.

Ocean ecosystem discrete time dynamics generated by ℓ-Volterra operators

2019 ◽  
Vol 12 (02) ◽  
pp. 1950015 ◽  
Author(s):  
U. A. Rozikov ◽  
S. K. Shoyimardonov
Keyword(s):  
Dynamical System ◽  
Fixed Points ◽  
Discrete Time ◽  
Volterra Operator ◽  
Saddle Points ◽  
Time Dynamics ◽  
Discrete Time Dynamical System ◽  
Starting Point ◽  
Ocean Ecosystem ◽  
Initial Starting

We consider a discrete-time dynamical system generated by a nonlinear operator (with four real parameters [Formula: see text]) of ocean ecosystem. We find conditions on the parameters under which the operator is reduced to a [Formula: see text]-Volterra quadratic stochastic operator mapping two-dimensional simplex to itself. We show that if [Formula: see text], then (under some conditions on [Formula: see text]) this [Formula: see text]-Volterra operator may have up to three or a countable set of fixed points; if [Formula: see text], then the operator has up to three fixed points. Depending on the parameters, the fixed points may be attracting, repelling or saddle points. The limit behaviors of trajectories of the dynamical system are studied. It is shown that independently on values of parameters and on initial (starting) point, all trajectories converge. Thus, the operator (dynamical system) is regular. We give some biological interpretations of our results.

Feedback Anticontrol of Discrete Chaos

1998 ◽  
Vol 08 (07) ◽  
pp. 1585-1590 ◽  
Author(s):  
Guanrong Chen ◽  
Dejian Lai
Keyword(s):  
Dynamical System ◽  
Discrete Time ◽  
State Feedback ◽  
Design Method ◽  
Control Design ◽  
Rigorous Approach ◽  
Discrete Time Dynamical System ◽  
Discrete Chaos ◽  
Simple Feedback ◽  
Discrete Time Dynamical Systems

In this paper, a simple feedback control design method earlier proposed by us for discrete-time dynamical systems is proved to be a mathematically rigorous approach for anticontrol of chaos, in the sense that any given discrete-time dynamical system can be made chaotic by the designed state-feedback controller along with the mod-operations.

scholarly journals A new class of hyperbolic variational–hemivariational inequalities driven by non-linear evolution equations

2020 ◽  
Vol 32 (1) ◽  
pp. 59-88
Author(s):  
STANISŁAW MIGÓRSKI ◽  
WEIMIN HAN ◽  
SHENGDA ZENG
Keyword(s):  
Dynamical System ◽  
Evolution Equations ◽  
Frictional Contact ◽  
Maximal Monotone ◽  
Contact Boundary ◽  
Hemivariational Inequalities ◽  
Response Condition ◽  
Linear Evolution ◽  
Linear Evolution Equation ◽  
Non Linear

The aim of the paper is to introduce and investigate a dynamical system which consists of a variational–hemivariational inequality of hyperbolic type combined with a non-linear evolution equation. Such a dynamical system arises in studies of complicated contact problems in mechanics. Existence, uniqueness and regularity of a global solution to the system are established. The approach is based on a new semi-discrete approximation with an application of a surjectivity result for a pseudomonotone perturbation of a maximal monotone operator. A new dynamic viscoelastic frictional contact model with adhesion is studied as an application, in which the contact boundary condition is described by a generalised normal damped response condition with unilateral constraint and a multivalued frictional contact law.

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