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A memristive hyperchaotic system without equilibrium.

Viet-Thanh Pham1, Christos Volos2, Lucia Valentina Gambuzza3

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Summary
This summary is machine-generated.

This study introduces a novel memristive system that lacks equilibria, demonstrating complex periodic, chaotic, and hyperchaotic dynamics. Circuit implementation validates its advanced hyperchaotic behavior.

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Area of Science:

  • Nonlinear dynamics
  • Chaos theory
  • Memristive systems

Background:

  • Memristive systems are crucial for advanced computing.
  • Understanding complex dynamics in memristive systems is essential for novel applications.
  • Existing models often exhibit equilibria, limiting dynamic range.

Purpose of the Study:

  • Introduce a novel memristive system.
  • Investigate its unique dynamical properties, including the absence of equilibria.
  • Explore the conditions for periodic, chaotic, and hyperchaotic behaviors.

Main Methods:

  • Numerical simulations: phase portraits, Lyapunov exponents, Poincaré sections.
  • Theoretical analysis of the system's equilibrium points.
  • Hardware circuit implementation for validation.

Main Results:

  • The proposed memristive system has no equilibrium points.
  • Periodic, chaotic, and hyperchaotic dynamics were observed within specific parameter ranges.
  • Circuit implementation successfully reproduced the predicted hyperchaotic dynamics.

Conclusions:

  • The novel memristive system offers a unique platform for studying complex dynamics.
  • The absence of equilibria contributes to a richer dynamic repertoire.
  • Validation through circuit implementation confirms its practical relevance for chaotic and hyperchaotic applications.