Emergent spatiotemporal complexity from reaction-diffusion hybridization: A new model for multistable pattern dynamics

Abstract

Abstract This paper introduces and analyzes a novel hybrid reaction–diffusion model that integrates key nonlinear features from the BVAM, Schnakenberg, and Gray–Scott systems. The proposed model captures both local activation and long-range inhibition through a complex interplay of autocatalytic and cross-inhibitory kinetics. We perform a detailed mathematical analysis including linear stability, Turing instability criteria, and Lyapunov exponent computations to characterize the onset of spatiotemporal complexity. Numerical simulations in both one and two spatial dimensions reveal a diverse spectrum of dynamic behaviors, ranging from Turing-type stationary patterns (spots, stripes, and labyrinths) to high-dimensional chaotic oscillations. The presence of positive Lyapunov exponents and a non-integer Kaplan–Yorke dimension confirms the emergence of deterministic chaos in both time and space. All simulations were conducted using a custom MATLAB implementation based on the Split-Step Fourier Method (SSFM). The results establish the hybrid model as a unifying framework capable of capturing rich pattern formation dynamics in nonlinear systems, with potential applications in developmental biology, chemical media, and ecological systems. This work extends classical reaction-diffusion theory by demonstrating how hybridized kinetics can lead to robust and tunable spatiotemporal chaos.