Spatiotemporal chaos in spatially extended fractional dynamical systems

• Published in: Communications in nonlinear science & numerical simulation 2023-05, Vol.119, p.107118, Article 107118
• Main Authors: Alqhtani, Manal, Owolabi, Kolade M., Saad, Khaled M., Pindza, Edson
• Format: Article
• Language: English
• Subjects: Fractional reaction–diffusion equations; Numerical experiments; Oscillatory patterns; Stability analysis
• ISSN: 1007-5704; 1878-7274
• DOI: 10.1016/j.cnsns.2023.107118

This study focuses on the study of spatiotemporal and chaotic behavior in an extended non-integer order dynamical systems which describe the spatial interaction between two biological or chemical species popularly referred to as prey and predator model. Such systems are somewhat sensitive to initial-value condition, and also exhibit irregular temporal behavior which often leads to the formation of irregular spatial patterns in high dimensions. Over the years, spatiotemporal dynamics of interacting biological/chemical species has been an active subject of discussion. To study the systems for Turing instability, we require to analyze the stability criteria of non-diffusive models at nontrivial state which is most relevant and feasible to our study. We compute the Lyapunov exponents and establish that the Kaplan Yorke dimension exists in the models. Two models of recurring interests are considered for spatiotemporal/complex pattern formations. •Formulation of viable numerical approximation techniques.•Numerical simulations in one and two dimensions.•Spatiotemporal and chaotic patterns formation.•Linear stability analysis of non-diffusive system.