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, cilt.114, sa.8, 2026 (SCI-Expanded, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 114 Sayı: 8
  • Basım Tarihi: 2026
  • Doi Numarası: 10.1007/s11071-026-12479-8
  • Dergi Adı: Nonlinear Dynamics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, INSPEC, zbMATH
  • Anahtar Kelimeler: 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
  • Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
  • Karadeniz Teknik Üniversitesi Adresli: Evet

Özet

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.