Piecewise-smooth Dynamical Systems: Theory and Applications

By M. D. Bernardo, C. Budd, A. Champneys, Piotr Kowalczyk. 2007

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Averaging theory at any order for computing limit cycles of discontinuous piecewise differential systems with many zones (2016, background): “ience. In fact, their associated diﬀerential systems are very usefulto model phenomena presenting abrupt switches such as electronic relays, mechanical impact, and neuronal networks, see for instance [2, 7, 23]. The extension of the averaging theory to discontinuous piecewise vector ﬁeld has been th”
Classes of Multiagent Q-learning Dynamics with epsilon-greedy Exploration (2010, methodology): “A general hybrid dynamical system (GHDS) is a system H = [P, Σ, J] with the following parts (Di Bernardo et al., 2008): • P is the set of index states or discrete dynamical system states; • Σ = p∈P Σ p is the set of ordinary differential equations (or flows) for index state p; • J = J p∈P is the…”