Bifurcations and Chaos in Simple Dynamical Systems

TL;DR

This paper explores how simple dynamical systems can exhibit chaotic behavior and bifurcations through mathematical modeling, highlighting the sensitive dependence on initial conditions and the discovery of simple chaotic systems.

Contribution

It provides a study of bifurcations and chaos in simple systems using mathematical models, emphasizing the behavior of periodic orbits and sensitive dependence on initial conditions.

Findings

Chaotic behavior can occur in very simple systems.

Periodic orbits are analyzed in continuous maps.

Sensitive dependence on initial conditions is demonstrated.

Abstract

Chaos is an active research subject in the fields of science in recent years. it is a complex and an erratic behavior that is possible in very simple systems. in the present day, the chaotic behavior can be observed in experiments. Many studies have been made in chaotic dynamics during the past three decades and many simple chaotic systems have been discovered. in this work-bifurcations and chaos in simple dynamical systems - the behavior of some simple dynamical systems is studied by constructing mathematical models. investigations are made on the periodic orbits for continuous maps and idea of sensitive dependence on initial conditions,which is the hallmark of chaos, is obtained.