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Multiscroll attractors by switching systems
E Campos-Cantón1, J G Barajas-Ramírez, G Solís-Perales
1Departamento de Físico Matemáticas, Universidad Autónoma de San Luis Potosí, Alvaro Obregón 64, Col. Centro, San Luis Potosí, Mexico.
Chaos (Woodbury, N.Y.)
|April 8, 2010
Summary
This study introduces unstable dissipative systems (UDSs), a novel class of three-dimensional dynamical systems. These systems utilize switching laws to generate complex multiscroll strange attractors with chaotic behavior.
Area of Science:
- Dynamical Systems Theory
- Nonlinear Dynamics
- Chaos Theory
Background:
- Understanding complex behaviors in three-dimensional dynamical systems is crucial.
- Existing models often struggle to generate intricate multiscroll attractors.
- Dissipative and unstable dynamics offer unique possibilities for complex system generation.
Purpose of the Study:
- To introduce a new class of three-dimensional dynamical systems termed unstable dissipative systems (UDSs).
- To demonstrate the capability of UDSs to generate diverse multiscroll strange attractors.
- To explore the chaotic behavior arising from these systems.
Main Methods:
- Development of a switching law for system control.
- Construction of piecewise-linear dynamical systems.
- Analysis of trajectories around saddle hyperbolic stationary points.
Main Results:
- Successfully generated various multiscroll strange attractors, both symmetric and asymmetric.
- Demonstrated that UDSs combine unstable "one-spiral" trajectories via switching.
- Confirmed chaotic behavior in the resulting multiscroll attractors.
Conclusions:
- Unstable dissipative systems provide a versatile framework for creating complex dynamical behaviors.
- The proposed switching mechanism effectively generates multiscroll attractors.
- These findings contribute to the understanding of chaos and complex dynamics in engineered systems.
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