# Li-Yorke chaos in nonautonomous Hopf bifurcation patterns - I

## TL;DR

This paper investigates the complex dynamics of nonautonomous systems undergoing Hopf bifurcation, revealing conditions for Li-Yorke chaos and expanding understanding of bifurcation patterns beyond autonomous cases.

## Contribution

It introduces a generalized nonautonomous Hopf bifurcation framework and analyzes the emergence of Li-Yorke chaos at bifurcation points.

## Key findings

- Li-Yorke chaos can occur at bifurcation points
- The attractor's characteristics relate to the Sacker and Sell spectrum
- Generalization of classical autonomous bifurcation patterns

## Abstract

We analyze the characteristics of the global attractor of a type of dissipative nonautonomous dynamical systems in terms of the Sacker and Sell spectrum of its linear part. The model gives rise to a pattern of nonautonomous Hopf bifurcation which can be understood as a generalization of the classical autonomous one. We pay special attention to the dynamics at the bifurcation point, showing the possibility of occurrence of Li-Yorke chaos in the corresponding attractor and hence of a high degree of unpredictability.