Analytic expressions for the unstable manifold at equilibrium points in dynamical systems of differential equations

1983 ◽  
Author(s):  
Fathi Abdel Salam ◽  
Aristotle Arapostathis ◽  
Pravin Varaiya
Keyword(s):  
Dynamical Systems ◽  
Differential Equations ◽  
Unstable Manifold ◽  
Equilibrium Points ◽  
Systems Of Differential Equations ◽  
Analytic Expressions

scholarly journals CYCLING CHAOS IN ONE-DIMENSIONAL COUPLED ITERATED MAPS

2002 ◽  
Vol 12 (08) ◽  
pp. 1859-1868 ◽  
Author(s):  
ANTONIO PALACIOS
Keyword(s):  
Dynamical Systems ◽  
Differential Equations ◽  
Fixed Points ◽  
Cell Systems ◽  
One Dimensional ◽  
Iterated Maps ◽  
Systems Of Differential Equations ◽  
Coupled Cell Systems ◽  
Cycling Chaos ◽  
Cycling Behavior

Cycling behavior involving steady-states and periodic solutions is known to be a generic feature of continuous dynamical systems with symmetry. Using Chua's circuit equations and Lorenz equations, Dellnitz et al. [1995] showed that "cycling chaos", in which solution trajectories cycle around symmetrically related chaotic sets, can also be found generically in coupled cell systems of differential equations with symmetry. In this work, we use numerical simulations to demonstrate that cycling chaos also occurs in discrete dynamical systems modeled by one-dimensional maps. Using the cubic map f (x, λ) = λx - x3 and the standard logistic map, we show that coupled iterated maps can exhibit cycles connecting fixed points with fixed points and periodic orbits with periodic orbits, where the period can be arbitrarily high. As in the case of coupled cell systems of differential equations, we show that cycling behavior can also be a feature of the global dynamics of coupled iterated maps, which exists independently of the internal dynamics of each map.

The Stability Study of Dynamic Systems Using the Leapunov Function Method

2019 ◽  
Vol 34 ◽  
pp. 123-128
Author(s):  
Dumitru Bălă
Keyword(s):  
Dynamical Systems ◽  
Differential Equations ◽  
Dynamic System ◽  
Dynamic Systems ◽  
Function Method ◽  
Autonomous Systems ◽  
Stability Study ◽  
Systems Of Differential Equations ◽  
Stability Theorems ◽  
The Stability

The paper includes the stability study of some dynamical systems given by systems of differential equations. The paper examines the stability of three dynamic systems using the Leapunov function method. The originality of the paper consists of how we choose the Leapunov function. We apply the stability theorems given by Leapunov for autonomous systems. Stability is an important property of a dynamic system that has applications in the technique.

SOLUTION OF SOME SYSTEMS OF DIFFERENTIAL EQUATIONS IN MATHEMATICAL SYSTEM MAPLE

2013 ◽  
Vol 1 (05) ◽  
pp. 58-65
Author(s):  
Yunona Rinatovna Krakhmaleva ◽  
◽  
Gulzhan Kadyrkhanovna Dzhanabayeva ◽  
Keyword(s):  
Differential Equations ◽  
Systems Of Differential Equations ◽  
Mathematical System

On decomposability of countable systems of differential equations

1993 ◽  
Vol 45 (10) ◽  
pp. 1598-1608
Author(s):  
A. M. Samoilenko ◽  
Yu. V. Teplinskii
Keyword(s):  
Differential Equations ◽  
Systems Of Differential Equations

scholarly journals Differential Games for an Infinite 2-Systems of Differential Equations

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1467
Author(s):  
Muminjon Tukhtasinov ◽  
Gafurjan Ibragimov ◽  
Sarvinoz Kuchkarova ◽  
Risman Mat Hasim
Keyword(s):  
Hilbert Space ◽  
Differential Equations ◽  
Differential Games ◽  
Differential Game ◽  
Infinite System ◽  
The State ◽  
Geometric Constraints ◽  
Control Parameters ◽  
Systems Of Differential Equations ◽  
Pursuit And Evasion

A pursuit differential game described by an infinite system of 2-systems is studied in Hilbert space l2. Geometric constraints are imposed on control parameters of pursuer and evader. The purpose of pursuer is to bring the state of the system to the origin of the Hilbert space l2 and the evader tries to prevent this. Differential game is completed if the state of the system reaches the origin of l2. The problem is to find a guaranteed pursuit and evasion times. We give an equation for the guaranteed pursuit time and propose an explicit strategy for the pursuer. Additionally, a guaranteed evasion time is found.

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