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Robust chaos in 3-D piecewise linear maps.

Mahashweta Patra¹, Soumitro Banerjee¹

¹Department of Physical Sciences, Indian Institute of Science Education and Research, Kolkata, Mohanpur Campus, 741246 West Bengal, India.

Chaos (Woodbury, N.Y.)

|January 3, 2019

Summary

This study demonstrates robust chaos in 3D piecewise linear maps, a phenomenon where chaotic attractors persist despite parameter changes. Conditions for its occurrence were derived by analyzing manifold interactions.

Area of Science:

Nonlinear dynamics
Chaos theory
Dynamical systems

Background:

Robust chaos is defined by the absence of periodic windows or coexisting attractors in parameter space.
Such attractors remain stable under small parameter variations due to minimal changes in Lyapunov exponents.
Previous research focused on robust chaos in 1D and 2D piecewise linear maps.

Purpose of the Study:

To demonstrate the occurrence of robust chaos in three-dimensional (3D) piecewise linear maps.
To derive the conditions necessary for the existence of robust chaos in these 3D systems.
To extend the understanding of robust chaos beyond lower-dimensional systems.

Main Methods:

Analysis of 3D piecewise linear maps.
Investigation of the interplay between stable and unstable manifolds.

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Derivation of conditions for robust chaos occurrence.

Main Results:

Occurrence of robust chaos is demonstrated in 3D piecewise linear maps.
Conditions for robust chaos are derived based on manifold dynamics.
The study extends the analysis of robust chaos to a higher-dimensional system.

Conclusions:

Robust chaos can exist in 3D piecewise linear maps.
The interplay of stable and unstable manifolds is crucial for robust chaos.
This work provides a foundation for studying robust chaos in more complex systems.