Counteracting dynamic degradation with an N-dimensional time-varying delay coupled chaotic map

Chaotic systems are valued across scientific fields for their nonlinear dynamics, yet their performance degrades significantly when implemented on low-precision hardware due to dynamical degradation. Therefore, this paper proposes an N-dimensional time-varying delay coupled method to reduce the dynamic degradation of digital chaotic systems, which uses a combined parameter-state perturbation and introduces delayed states in both the state space and the parameter space. This mechanism ensures that delayed states directly modulate the current system evolution while indirectly destabilizing control parameters, thereby effectively disrupting periodic attractors and enhancing trajectory divergence. Furthermore, the model exhibits strong generalizability, enabling transformation of arbitrary 1D seed maps into high-dimensional chaotic systems with scalable complexity. The experimental validation involves the construction of 2D and 3D variants using different seed maps, followed by a comprehensive evaluation using experiments such as Lyapunov exponential analysis, bifurcation diagrams, and entropy metrics. Extensive simulations and performance tests show that our model has strong chaotic properties, still achieves desirable dynamics at lower accuracy, and is competitive with other schemes.