Mathematical physiology
Oscillatority of Nonlinear Systems with Static Feedback
SIAM Journal on Control and Optimization
Oscillation analysis of linearly coupled piecewise affine systems
Proceedings of the 13th ACM international conference on Hybrid systems: computation and control
Delay robustness in consensus problems
Automatica (Journal of IFAC)
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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.