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A class of memristive feedback-based cascade hyperchaotic maps

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  • Qin, Minghong
  • Lai, Qiang

Abstract

Memristor can effectively enhance the nonlinearity of simple systems and maps, yielding complex dynamic behaviors, which have been widely used for the chaos generation and regulation. This paper introduces a memristive feedback term into a non-chaotic simple cascade map, successfully obtaining hyperchaos with multiple positive Lyapunov exponents. Three hyperchaotic maps are derived as examples, which are capable of producing complex dynamics. Through numerical analysis, the dynamics depend on non-memristive, memristive parameters and initial conditions are investigated, revealing rich hyperchaotic and multistability behaviors. A digital circuit platform is established to verify the physical existence and feasibility of the proposed hyperchaotic maps. Utilizing the hyperchaotic sequences produced from those maps, some PRNGs with high randomness are designed, and NIST tests show their superiority. Furthermore, a chaos-based PSO algorithm is proposed. And, some standard test functions and robot path planning task demonstrate the application value of the proposed study.

Suggested Citation

  • Qin, Minghong & Lai, Qiang, 2026. "A class of memristive feedback-based cascade hyperchaotic maps," Chaos, Solitons & Fractals, Elsevier, vol. 206(C).
    • Handle: RePEc:eee:chsofr:v:206:y:2026:i:c:s0960077926000925
    DOI: 10.1016/j.chaos.2026.117951
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