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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.)
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Summary
This summary is machine-generated.

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.

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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.