Lyapunov exponents of hybrid stochastic heat equations

Explicit expressions for the Lyapunov exponents of certain Markov processes

A method for the explicit computation of the Lyapunov exponents of certain Markov processes is developed. Its utility is demonstrated by an application to two-dimensional random evolution differential equations. Our approach exploits the relation between the Lyapunov exponent and the p-moment Lyapunov exponents, as was first observed and studied by Arnold [1]. The p-moment Lyapunov exponent is ...

Lyapunov exponents of linear stochastic functional differential equations driven by semimartingales

Qr-based Methods for Computing Lyapunov Exponents of Stochastic Differential Equations

Lyapunov exponents (LEs) play a central role in the study of stability properties and asymptotic behavior of dynamical systems. However, explicit formulas for them can be derived for very few systems, therefore numerical methods are required. Such is the case of random dynamical systems described by stochastic differential equations (SDEs), for which there have been reported just a few numerica...

Stability Index for Invariant Manifolds of Stochastic Systems

A lot of works has been devoted to stability analysis of a stationary point for linear and non-linear systems of stochastic di erential equations. Here we consider the stability of an invariant compact manifold of a non-linear system. To this end we derive a linearized system for orthogonal displacements of a solution from the manifold. We introduce notions of Lyapunov exponents, moment Lyapuno...

Stochastic Hybrid Systems with Renewal Transitions: Moment Analysis with Application to Networked Control Systems with Delays

We consider Stochastic Hybrid Systems (SHSs) for which the lengths of times that the system stays in each mode are independent random variables with given distributions. We propose an approach based on a set of Volterra equations to compute any statistical moment of the state of the SHS. Moreover, we provide a method to compute the Lyapunov exponents of a given degree, i.e., the exponential rat...