Synthesizing the L\"{u} attractor by parameter-switching

TL;DR

This paper presents a numerical method to synthesize the Lü attractor by switching parameters in the Lorenz and Chen systems, demonstrating the ability to generate complex attractors from finite parameter sets.

Contribution

It introduces a parameter-switching algorithm to synthesize the Lü attractor from generalized Lorenz and Chen systems, expanding the methods for attractor synthesis.

Findings

Successful numerical synthesis of the Lü attractor.

Validation of the parameter-switching method for attractor generation.

Applicability to systems with finite parameter sets.

Abstract

In this letter we synthesize numerically the L\"{u} attractor starting from the generalized Lorenz and Chen systems, by switching the control parameter inside a chosen finite set of values on every successive adjacent finite time intervals. A numerical method with fixed step size for ODEs is used to integrate the underlying initial value problem. As numerically and computationally proved in this work, the utilized attractors synthesis algorithm introduced by the present author before, allows to synthesize the L\"{u} attractor starting from any finite set of parameter values.