Principles of Discontinuous Dynamical Systems

Discontinuous dynamical systems have played an important role in both theory and applications during the last several decades. This is still an area of active research and techniques to make the applications more effective are an ongoing topic of interest. Principles of Discontinuous Dynamical Syste...

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Main Author: Akhmet, Marat
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: New York, NY Springer New York 2010, 2010
Edition:1st ed. 2010
Subjects:
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
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245 0 0 |a Principles of Discontinuous Dynamical Systems  |h Elektronische Ressource  |c by Marat Akhmet 
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505 0 |a Description of the System with Fixed Moments of Impulses and Its Solutions -- Stability and Periodic Solutions of Systems with Fixed Moments of Impulses -- Basics of Linear Systems -- Nonautonomous Systems with Variable Moments of Impulses -- Differentiability Properties of Nonautonomous Systems -- Periodic Solutions of Nonlinear Systems -- Discontinuous Dynamical Systems -- Perturbations and Hopf Bifurcation of a Discontinuous Limit Cycle -- Chaos and Shadowing 
653 |a Dynamical Systems and Ergodic Theory 
653 |a Ergodic theory 
653 |a Partial Differential Equations 
653 |a Partial differential equations 
653 |a Ordinary Differential Equations 
653 |a Differential equations 
653 |a Dynamics 
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520 |a Discontinuous dynamical systems have played an important role in both theory and applications during the last several decades. This is still an area of active research and techniques to make the applications more effective are an ongoing topic of interest. Principles of Discontinuous Dynamical Systems is devoted to the theory of differential equations with variable moments of impulses. It introduces a new strategy of implementing an equivalence to systems whose solutions have prescribed moments of impulses and utilizing special topologies in spaces of piecewise continuous functions. The achievements obtained on the basis of this approach are described in this book. The text progresses systematically, by covering preliminaries in the first four chapters. This is followed by more complex material and special topics such as Hopf bifurcation, Devaney's chaos, and the shadowing property are discussed in the last two chapters. This book is suitable for researchers and graduate students in mathematics and also in diverse areas such as biology, computer science, and engineering who deal with real world problems