Titlebook: Qualitative Theory of Hybrid Dynamical Systems; Alexey S. Matveev,Andrey V. Savkin Book 2000 Springer Science+Business Media New York 2000

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Qualitative Analysis of Some Simple Hybrid Dynamical Systems, of some theorems in this book may look quite complicated, they simply serve as means to reach our ultimate goal, set forward by the initial motivation and intuition. In this chapter, we shall use a number of relatively simple examples to explain the intuitive ideas underlying the topics of this book.

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Two-Dimensional Hybrid Dynamical Systems,eory developed in Chapter 3 is applied to establish an analog of the classic Poincaré-Bendixon theorem. This theorem states that, for a planar autonomous ordinary differential equation, any trajectory lying in a bounded invariant domain either

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monogamy

Limit Cycles in Hybrid Dynamical Systems with Constant Derivatives: Examples,ral theory developed in Chapter 5 makes qualitative analysis of these systems quite an easy task. For any of them, we show that there exist a finite number of limit cycles attracting all the trajectories of the system and compute this number. For each cycle, the region of attraction is found.

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978-1-4612-7114-7Springer Science+Business Media New York 2000

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General Theory of Multivalued Differential Automata,tinuous one obeys a definite ordinary differential equation. Transition to another discrete state causes an alteration of this equation. The discrete state keeps its value, while the continuous one remains in a certain specific region and evolves as soon as this region is left. Furthermore, we intro

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Two-Dimensional Hybrid Dynamical Systems,eory developed in Chapter 3 is applied to establish an analog of the classic Poincaré-Bendixon theorem. This theorem states that, for a planar autonomous ordinary differential equation, any trajectory lying in a bounded invariant domain either