Discrete Dynamical Systems with Random Impulses

TL;DR

This paper investigates the stability of discrete dynamical systems with random impulses, demonstrating that splitting and average contraction properties ensure stability, supported by simple-to-verify examples.

Contribution

It introduces conditions like splitting and average contraction that guarantee stability in systems with random impulses, with practical examples for verification.

Findings

Splitting property guarantees system stability.

Average contraction property ensures stability.

Examples show easy verification of these properties.

Abstract

We study the behaviour of discrete dynamical systems generated by a continuous map $f$ of a compact real interval into itself where at randomly chosen times a function different from $f$ - so called impulse function is applied. We show that both the splittting property and the average contraction property guarantee the stability of the system. We give a number of examples where the verification of these properties is simple.