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Journal of Mathematical Chemistry

, Volume 57, Issue 2, pp 638–654 | Cite as

Complex pattern formation arising from wave instabilities in a three-agent chemical system with superdiffusion

  • Alain MvogoEmail author
  • Jorge E. Macías-Díaz
Original Paper
  • 55 Downloads

Abstract

This work investigates analytically and numerically the wave instabilities in a three-agent chemical system undergoing anomalous diffusion. Anomalous diffusion is modeled using higher-dimensional space-fractional operators. The model considers one activator and two inhibitors, and it is a superdiffusive extension of some reaction-diffusion systems in the literature (Phys D Nonlinear Phenom 199(1–2):264–277, 2004). The model under investigation is presented in generic form as a three-species reaction-diffusion system, so that it has broad applicability to a wide range of chemical and biological systems. A weakly nonlinear analysis is performed, dispersive curves of eigenvalues are plotted and their behavior is analyzed. This analysis reveals that the critical value of the wave number for wave instability increases when the superdiffusive exponent decreases. The numerical scheme is performed and some numerical simulations are conducted as evidence of the analytical predictions. We show how the evolution of spatio-temporal patterns is related to meaningful parameters. In particular, we demonstrate that the system exhibits the coexistence of regular and irregular structures, forming complex patterns that are not familiar in standard reaction-diffusion systems.

Keywords

Wave instability Chemical system Anomalous diffusion Space-fractional operators Superdiffusive exponent Reaction-diffusion systems Pattern formation Regular and irregular structures 

Notes

Acknowledgements

One of us (AM) Acknowledges fruitful discussions with Professor K. Showalter of the University of West Virginia, USA, during the event “Hands-on Research in Complex Systems School” at the Abdus Salam International Centre for Theoretical Physics (ICTP). He also Acknowledges the invitation and Financial support from the ICTP.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Laboratory of Biophysics, Department of Physics Faculty of ScienceUniversity of Yaounde ICameroonSouth Africa
  2. 2.The Abdus Salam International Center For Theoretical PhysicsTriesteItaly
  3. 3.Departamento de Matemáticas y FísicaUniversidad Autónoma de AguascalientesAguascalientesMexico

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