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A novel strange attractor with a stretched loop


This short paper introduces a new 3D strange attractor topologically different from any other known chaotic attractors. The intentionally constructed model of three autonomous first-order differential equations derives from the coupling-induced complexity of the well-established 2D Lotka–Volterra oscillator. Its chaotification process via an anti-equilibrium feedback allows the exploration of a new domain of dynamical behavior including chaotic patterns. To focus a rapid presentation, a fixed set of parameters is selected linked to the widest range of dynamics. Indeed, the new system leads to a chaotic attractor exhibiting a double scroll bridged by a loop. It mutates to a single scroll with a very stretched loop by the variation of one parameter. Indexes of stability of the equilibrium points corresponding to the two typical strange attractors are also investigated. To encompass the global behavior of the new low-dimensional dissipative dynamical model, diagrams of bifurcation displaying chaotic bubbles and windows of periodic oscillations are computed. Besides, the dominant exponent of the Lyapunov spectrum is positive reporting the chaotic nature of the system. Eventually, the novel chaotic model is suitable for digital signal encryption in the field of communication with a rich set of keys.

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The author is grateful to two anonymous reviewers for their valuable comments and constructive feedbacks.

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Correspondence to Safieddine Bouali.

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Bouali, S. A novel strange attractor with a stretched loop. Nonlinear Dyn 70, 2375–2381 (2012).

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  • Chaotification
  • Lotka–Volterra-like oscillator
  • 3D nonlinear system
  • Strange attractor
  • Diagram of bifurcation
  • Lyapunov exponent