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

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Owolabi K. M., Akgül A., Alisherov F.

Nonlinear Dynamics, vol.114, no.8, 2026 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 114 Issue: 8
  • Publication Date: 2026
  • Doi Number: 10.1007/s11071-026-12479-8
  • Journal Name: Nonlinear Dynamics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, INSPEC, zbMATH
  • Keywords: Clean Water and Sanitation, Climate Action, Hybrid dynamical model, Industry, Innovation and Infrastructure, Life Below Water, Life on Land, Lyapunov exponents, Reaction-diffusion systems, Spatiotemporal chaos, Sustainable Cities and Communities, Turing patterns
  • Open Archive Collection: AVESIS Open Access Collection
  • Karadeniz Technical University Affiliated: Yes

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.