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On multistability behavior of unstable dissipative systems.

A Anzo-Hernández¹, H E Gilardi-Velázquez², E Campos-Cantón²

¹Cátedras CONACYT - Benemérita Universidad Autónoma de Puebla - Facultad de Ciencias Físico-Matemáticas, Benemerita Universidad Autónoma de Puebla, Avenida San Claudio y 18 Sur, Colonia San Manuel, 72570 Puebla, Mexico.

Chaos (Woodbury, N.Y.)

|April 2, 2018

Summary

We introduce unstable dissipative systems capable of multi-stable behavior, where system trajectories depend on initial conditions. These systems generate piecewise linear (PWL) chaotic trajectories with multiple scrolls.

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Area of Science:

Nonlinear dynamics
Chaos theory
Dynamical systems

Background:

Unstable dissipative systems exhibit complex dynamics.
Multi-stability in dynamical systems is dependent on initial conditions.
Piecewise linear (PWL) systems can generate chaotic behavior.

Purpose of the Study:

To present unstable dissipative systems capable of multi-stable behavior.
To explore the generation of chaotic trajectories with multiple wings or scrolls using PWL systems.
To investigate parameter ranges for multi-stability and multiscroll chaotic trajectories in PWL systems.

Main Methods:

Developing PWL systems derived from unstable dissipative systems.
Proposing a specific structure for the PWL system where linear and switching functions are parameterized.
Analyzing the system's behavior across a range of parameter values.

Main Results:

Demonstrated that unstable dissipative systems can lead to multi-stable behavior.
Showcased the generation of chaotic trajectories with multiple wings or scrolls in the proposed PWL system.
Identified parameter ranges that yield multi-stability and multiscroll chaotic attractors.

Conclusions:

Unstable dissipative systems provide a foundation for multi-stable dynamical behaviors.
The proposed parameterized PWL system effectively generates multiscroll chaotic attractors.
Parameter tuning in PWL systems offers control over chaotic dynamics and multi-stability.