scholarly journals On the dynamics of nonautonomous periodic general dynamical systems and differential inclusions

2006 ◽  
Vol 224 (1) ◽  
pp. 1-38 ◽  
Author(s):  
Desheng Li ◽  
Peter E. Kloeden
Keyword(s):  
Dynamical Systems ◽  
Differential Inclusions

On the Dynamics of Nonautonomous General Dynamical Systems and Differential Inclusions

2007 ◽  
Vol 16 (5-6) ◽  
pp. 651-671 ◽  
Author(s):  
Desheng Li ◽  
Yejuan Wang ◽  
Suyun Wang
Keyword(s):  
Dynamical Systems ◽  
Differential Inclusions

scholarly journals Quadratic Stability of Non-Linear Systems Modeled with Norm Bounded Linear Differential Inclusions

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1432
Author(s):  
Mutti-Ur Rehman ◽  
Jehad Alzabut ◽  
Arfan Hyder
Keyword(s):  
Dynamical Systems ◽  
Differential Inclusions ◽  
Bounded Linear ◽  
Linear Dynamical Systems ◽  
Quadratic Stability ◽  
Linear Differential Inclusions ◽  
Non Linear ◽  
Linear Differential ◽  
The Stability ◽  
Non Linear System

In this article we present an ordinary differential equation based technique to study the quadratic stability of non-linear dynamical systems. The non-linear dynamical systems are modeled with norm bounded linear differential inclusions. The proposed methodology reformulate non-linear differential inclusion to an equivalent non-linear system. Lyapunov function demonstrate the existence of a symmetric positive definite matrix to analyze the stability of non-linear dynamical systems. The proposed method allows us to construct a system of ordinary differential equations to localize the spectrum of perturbed system which guarantees the stability of non-linear dynamical system.

scholarly journals Bounded Motions of the Dynamical Systems Described by Differential Inclusions

2009 ◽  
Vol 2009 ◽  
pp. 1-9
Author(s):  
Nihal Ege ◽  
Khalik G. Guseinov
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Differential Inclusion ◽  
Differential Inclusions ◽  
Sufficient Conditions ◽  
Invariant Sets ◽  
Control Vector ◽  
Upper Semicontinuous ◽  
Right Hand ◽  
The Right

The boundedness of the motions of the dynamical system described by a differential inclusion with control vector is studied. It is assumed that the right-hand side of the differential inclusion is upper semicontinuous. Using positionally weakly invariant sets, sufficient conditions for boundedness of the motions of a dynamical system are given. These conditions have infinitesimal form and are expressed by the Hamiltonian of the dynamical system.

scholarly journals Turnpike Properties for Dynamical Systems Determined by Differential Inclusions

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2326
Author(s):  
Alexander J. Zaslavski
Keyword(s):  
Dynamical Systems ◽  
Finite Number ◽  
Differential Inclusion ◽  
Continuous Time ◽  
Differential Inclusions ◽  
Mathematical Economics ◽  
Symmetric Property

In this paper, we study the turnpike phenomenon for trajectories of continuous-time dynamical systems generated by differential inclusions, which have a prototype in mathematical economics. In particular, we show that, if the differential inclusion has a certain symmetric property, the turnpike possesses the corresponding symmetric property. If we know a finite number of approximate trajectories of our system, then we know the turnpike and this information can be useful if we need to find new trajectories of our system or their approximations.

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