The LaSalle theorem for coupled systems of differential equations

2017 ◽  
Author(s):  
Jiqiang Feng ◽  
Guixiang Lai ◽  
Sitian Qin ◽  
Zheng Xu
Keyword(s):  
Differential Equations ◽  
Coupled Systems ◽  
Systems Of Differential Equations ◽  
Lasalle Theorem

Homoclinic solutions for coupled systems of differential equations

1985 ◽  
Vol 99 (3-4) ◽  
pp. 319-328 ◽  
Author(s):  
P. Grindrod ◽  
B. D. Sleeman
Keyword(s):  
Differential Equations ◽  
Hamiltonian Systems ◽  
Reaction Diffusion ◽  
Homoclinic Orbits ◽  
Homoclinic Solutions ◽  
Coupled Systems ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Systems Of Differential Equations ◽  
Unmyelinated Nerve

SynopsisTopological ideas based on the notion of flows and Wazewski sets are used to establish the existence of homoclinic orbits to a class of Hamiltonian systems. The results, as indicated, are applicable to a variety of reaction diffusion equations including models of bundles of unmyelinated nerve axons.

scholarly journals A New Approach to the Method of Lyapunov Functionals and Its Applications

2013 ◽  
Vol 2013 ◽  
pp. 1-12
Author(s):  
Yunguo Jin ◽  
Shouming Zhong
Keyword(s):  
Differential Equations ◽  
Global Stability ◽  
Epidemic Model ◽  
Lyapunov Functions ◽  
Stage Structure ◽  
Host Population ◽  
Coupled Systems ◽  
Lyapunov Functionals ◽  
New Approach ◽  
Systems Of Differential Equations

We show some results which can replace the graph theory used to construct global Lyapunov functions in some coupled systems of differential equations. We present an example of an epidemic model with stage structure and latency spreading in a heterogeneous host population and obtain a more general threshold for the extinction and persistence of a disease. Using some results obtained by mathematical induction and suitable Lyapunov functionals, we prove the global stability of the endemic equilibrium. For some coupled systems of differential equations, by a similar approach to the discussion of the epidemic model, the conditions of threshold property or global stability can be established without the assumption that the relative matrix is irreducible.

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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