Evaluation of the Lyapunov exponent for generalized linear second-order exponential systems

TL;DR

This paper investigates the Lyapunov exponent in generalized linear second-order exponential systems, providing new insights into the asymptotic growth rate of such stochastic dynamical systems.

Contribution

It introduces novel methods for evaluating the Lyapunov exponent in systems with exponential or zero entries in the state transition matrix.

Findings

Derived formulas for the Lyapunov exponent in specific cases

Extended understanding of growth behavior in stochastic systems

Provided analytical tools for system stability analysis

Abstract

We consider generalized linear stochastic dynamical systems with second-order state transition matrices. The entries of the matrix are assumed to be either independent and exponentially distributed or equal to zero. We give an overview of new results on evaluation of asymptotic growth rate of the system state vector, which is called the Lyapunov exponent of the system.