PhD theses (D1-8)
Local interactions in space can give rise to large scale spatio temporal patterns (e.g. (spiral) waves, spatio-temporal chaos (turbulence), stationary (Turing-type) patterns and transitions between these modes). Their occurrence and properties are largely independent of the precise interaction structure. They are indeed seen to occur at many organizational levels of biotic systems.
Space can be either 'real' space or a state space, e.g. 'phenotype space' in models of speciation or 'shape space' in immunological models of shape-based receptor interactions. We show that such spatio-temporal patterns have important consequences for fundamental bioinformatic processes.
We studied the general properties of spiral waves (38,54,58) e.g. their initiation by geometry (14) and by high frequency stimulation near in-excitable boundaries (10,26) (later experimentally found in cardiac tissue and the BZ reaction) and possible instabilities leading to turbulence. We found and characterized spiral breakup by either wave-back (8,40,49) or wave front (59) instabilities in excitable systems and by convection in oscillatory systems (66) , and (in 3 D) by rotational anisotropy (9,39) and by transversal heterogeneity (11). Spiral waves and these instabilities appear to be responsible for cardiac arrythmias and fibrillaton, occur in the retina and in e.g. intra cellular calcium waves, play an important role in Dictyostelium development , and define new levels of selection in eco-evolutionary systems .