Oscillation analysis of linearly coupled piecewise affine systems: Application to spatio-temporal neuron dynamics

This paper discusses oscillation analysis of (a large number of) linearly coupled piecewise affine (PWA) systems, motivated by various kinds of reaction–diffusion systems including cell-signaling dynamics and neural dynamics. We derive a sufficient condition under which the system shows an oscillatory behavior called Y-oscillation. It is known that the analysis of PWA systems is difficult due to their switching nature. An important feature of the result obtained is that, under the assumption that every subsystem has a specific property in common, the criteria can be rewritten in terms of coupling topology in an easily checkable way, so it is applicable to large scale systems. The results obtained are applied to theoretical investigation of the cardiac action potential generation/propagation represented by spatio-temporal FitzHugh–Nagumo equations.