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Oscillatory periodic pattern dynamics in hyperbolic reaction-advection-diffusion models
Giancarlo Consolo1, Carmela Curró1, Gabriele Grifó1
1Department of Mathematical, Computer, Physical and Earth Sciences, University of Messina (Italy) V.le F. Stagno D'Alcontres 31, I-98166 Messina, Italy.
Physical Review. E
|April 16, 2022
Summary
Inertial effects in reaction-advection-diffusion systems significantly influence oscillatory patterns. These effects alter pattern amplitude, wavelength, frequency, and stability, expanding instability regions.
Area of Science:
- Mathematical modeling
- Theoretical physics
- Chemical kinetics
Background:
- Reaction-advection-diffusion systems model complex spatio-temporal phenomena.
- Oscillatory patterns arise in various natural systems, including vegetation dynamics.
- Inertial effects are often neglected but can significantly impact system dynamics.
Purpose of the Study:
- To investigate the role of inertial effects in two-species hyperbolic reaction-advection-diffusion systems.
- To understand how inertia influences the formation and stability of oscillatory periodic patterns.
- To analyze the impact of inertia on pattern characteristics like amplitude and wavelength.
Main Methods:
- Linear stability analysis to identify conditions for wave (oscillatory Turing) instability.
- Multiple-scale weakly nonlinear analysis to derive the governing equation for pattern amplitude.
- Numerical simulations and analytical comparisons using a hyperbolic generalization of the extended Klausmeier model.
Main Results:
- A cubic complex Ginzburg-Landau (CCGL) equation governs pattern evolution, with coefficients dependent on inertial times.
- Inertia enlarges the parameter space for wave instability.
- Inertial effects modulate pattern amplitude, wavelength, angular frequency, and stability of phase-winding solutions.
Conclusions:
- Inertia plays a crucial role in both transient pattern formation and the steady-state characteristics of oscillatory patterns.
- The study highlights the importance of including inertial effects in modeling complex spatio-temporal systems.
- Findings have implications for understanding pattern dynamics in ecological and chemical systems.
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