Dual-time variable dual-pulse intermittent control strategy of a novel six-dimensional memristive hyper-chaotic system

This paper constructs a novel six-dimensional hyper-chaotic system by incorporating a flux-controlled memristor as a nonlinear feedback element into an existing five-dimensional chaotic system. The dynamical characteristics of the proposed system are systematically investigated by means of Lyapunov exponent spectra, Kaplan–Yorke dimension calculation, bifurcation diagrams, Poincaré maps, and power spectral analysis, showing that the system exhibits rich parameter-dependent behaviors. Its physical implementability is validated via analog circuit simulation. To stabilize the resulting hyper-chaotic dynamics, a dual-time variable dual-pulse intermittent control strategy is proposed, in which the widths of the controlled and uncontrolled phases decrease monotonically with a fixed step size, while the two impulsive gains decay exponentially. Sufficient conditions for exponential stability are derived via Lyapunov theory and formulated as linear matrix inequalities feasibility problems. Numerical simulations show that the proposed controller can rapidly stabilize both the newly constructed six-dimensional memristive hyper-chaotic system and a four-dimensional hyper-chaotic financial system, demonstrating broad applicability to nonlinear dynamical models arising in engineering and economics.