Propagation failure in discrete reaction-diffusion system based on the butterfly bifurcation

Area of Science:

• Mathematical modeling
• Complex systems
• Pattern formation

Background:

• Reaction-diffusion systems model species interactions in various scientific fields.
• Traveling waves/fronts represent spatial transitions between equilibrium states.
• Propagation velocity depends on reaction nonlinearities, diffusion, and lattice structures.

Purpose of the Study:

• Investigate propagation failure in 1D traveling fronts within systems exhibiting the butterfly bifurcation.
• Analyze how spatial discreteness affects different traveling fronts.
• Extend the analysis to 2D lattices and planar fronts.

Main Methods:

• Analysis of reaction-diffusion systems with three stable coexisting equilibrium states.
• Study of the butterfly bifurcation and its impact on front propagation.
• Examination of 1D and 2D lattice structures and front orientations.

Main Results:

• Spatial discreteness affects the three types of 1D traveling fronts distinctly.
• Propagation failure regions introduce complexity to the butterfly diagram.
• In 2D lattices, both propagation failure and preferred orientations influence pattern evolution.

Conclusions:

• The study highlights the significant impact of spatial discreteness on reaction-diffusion front dynamics.
• Understanding propagation failure is crucial for predicting pattern formation in discrete systems.
• Lattice structure and orientation are key factors in 2D pattern evolution.