On the Almost Sure Stability of Linear Stochastic Distributed-Parameter Dynamical Systems

1966 ◽  
Vol 33 (1) ◽  
pp. 182-186 ◽  
Author(s):  
P. K. C. Wang
Keyword(s):  
Dynamical Systems ◽  
Asymptotic Stability ◽  
Integral Equations ◽  
Sufficient Conditions ◽  
Distributed Parameter ◽  
Almost Sure Stability ◽  
Partial Differential ◽  
Stochastic Parameters

In this paper, sufficient conditions for almost sure stability and asymptotic stability of certain classes of linear stochastic distributed-parameter dynamical systems are derived. These systems are described by a set of linear partial differential or differential-integral equations with stochastic parameters. Various examples are given to illustrate the application of the main results.

Stability of Continuous Dynamic Systems With Parametric Excitation

1969 ◽  
Vol 36 (2) ◽  
pp. 212-216 ◽  
Author(s):  
J. R. Dickerson ◽  
T. K. Caughey
Keyword(s):  
Partial Differential Equations ◽  
Asymptotic Stability ◽  
Differential Equations ◽  
Dynamic Systems ◽  
Parametric Excitation ◽  
Sufficient Conditions ◽  
Partial Differential ◽  
Continuous Dynamic

A Lyapunov-type approach is used to establish sufficient conditions guaranteeing the asymptotic stability of a class of partial differential equations with parametric excitation.

FINITE DIMENSIONALITY OF ATTRACTORS FOR NON-AUTONOMOUS DYNAMICAL SYSTEMS GIVEN BY PARTIAL DIFFERENTIAL EQUATIONS

2004 ◽  
Vol 04 (03) ◽  
pp. 385-404 ◽  
Author(s):  
J. A. LANGA ◽  
B. SCHMALFUSS
Keyword(s):  
Partial Differential Equations ◽  
Dynamical Systems ◽  
Differential Equations ◽  
Sufficient Conditions ◽  
Fractal Dimensionality ◽  
Natural Generalization ◽  
Pullback Attractor ◽  
Compact Sets ◽  
Qualitative Properties ◽  
Partial Differential

In the last decade, the concept of pullback attractor has become one of the usual tools to describe some qualitative properties of non-autonomous partial differential equations. A pullback attractor is a family of compact sets, invariant for the corresponding process related to the equation, and attracting from the past, and it assumes a natural generalization of the now classical concept of global attractor for autonomous partial differential equations. In this work we give sufficient conditions in order to prove the finite Hausdorff and fractal dimensionality of pullback attractors for non-autonomous infinite dimensional dynamical systems, and we apply our results to a generalized non-autonomous partial differential equation of Navier–Stokes type.

scholarly journals Hybrid nonnegative and computational dynamical systems

2002 ◽  
Vol 8 (6) ◽  
pp. 493-515 ◽  
Author(s):  
Wassim M. Haddad ◽  
Vijaysekhar Chellaboina ◽  
Sergey G. Nersesov
Keyword(s):  
Dynamical Systems ◽  
Asymptotic Stability ◽  
Conservation Laws ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Hybrid Structures ◽  
Stability Criteria ◽  
General Stability ◽  
Feedback Interconnections ◽  
Flow Laws

Nonnegative and Compartmental dynamical systems are governed by conservation laws and are comprised of homogeneous compartments which exchange variable nonnegative quantities of material via intercompartmental flow laws. These systems typically possess hierarchical (and possibly hybrid) structures and are remarkably effective in capturing the phenomenological features of many biological and physiological dynamical systems. In this paper we develop several results on stability and dissipativity of hybrid nonnegative and Compartmental dynamical systems. Specifically, usinglinearLyapunov functions we develop sufficient conditions for Lyapunov and asymptotic stability for hybrid nonnegative dynamical systems. In addition, usinglinearandnonlinearstorage functions withlinearhybrid supply rates we developnewnotions of dissipativity theory for hybrid nonnegative dynamical systems. Finally, these results are used to develop general stability criteria for feedback interconnections of hybrid nonnegative dynamical systems.

Conditions for the local and global asymptotic stability of the time–fractional Degn–Harrison system

2020 ◽  
Vol 21 (7-8) ◽  
pp. 749-759
Author(s):  
Rachida Mezhoud ◽  
Khaled Saoudi ◽  
Abderrahmane Zaraï ◽  
Salem Abdelmalek
Keyword(s):  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Lyapunov Method ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Linearization Method ◽  
Direct Lyapunov Method ◽  
Fractional Systems ◽  
Reaction Diffusion Model ◽  
Theoretical Results

AbstractFractional calculus has been shown to improve the dynamics of differential system models and provide a better understanding of their dynamics. This paper considers the time–fractional version of the Degn–Harrison reaction–diffusion model. Sufficient conditions are established for the local and global asymptotic stability of the model by means of invariant rectangles, the fundamental stability theory of fractional systems, the linearization method, and the direct Lyapunov method. Numerical simulation results are used to illustrate the theoretical results.

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