Topological Characterization of
It is well established both numerically and experimentally
that nonlinear systems involving diffusion, chemotaxis, and/or
convection mechanisms can generate complicated time-dependent patterns.
Since this phenomenon is global in nature, obtaining a quantitative
mathematical characterization that to some extent records or preserves
the geometric structures of the complex patterns is difficult. Here we
show that using algebraic topology, in particular homology, we can
measure Lyapunov exponents that imply the existence of spatial-temporal
chaos and suggest a tentative step towards the classification and/or
identification of patterns within the FitzHugh-Nagumo system.