Design and hardware implementation of extreme multistable chaotic systems

Abstract Extreme multistable chaotic systems, capable of generating signals with diverse amplitudes, offer significant advantages for secure communications. However, making any 3-D quadratic continuous chaotic system exhibit extreme multistability without increasing the system’s dimensionality or complexity remains a challenging task. To address this issue, this paper proposes a novel design method, termed the Generalized Equilibrium Point Expansion Method (GEPEM). GEPEM is governed by three design criteria: trigonometric substitution, equilibrium solvability preservation, and chaos control. GEPEM offers the advantages of broad generality and strong model generalization, without requiring additional state variables. We apply GEPEM to the unified chaotic system and the Sprott B system, and numerical simulations demonstrate an infinite number of coexisting double-wing attractors along various spatial axes. Furthermore, coexisting self-oscillating, time-dependent multiwing attractors are observed. To verify the feasibility and engineering practicality of GEPEM, we conduct circuit simulations and develop a DSP-based platform. Finally, we design a PRNG based on the multistable chaotic system. With all P-values exceeding the 0.01 threshold in the NIST SP 800-22 tests, the designed PRNG exhibits excellent randomness.