Principles of Discontinuous Dynamical Systems

1. Front Matter

   Pages i-xi

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2. Introduction

   • Marat Akhmet

   Pages 1-6

3. Description of the System with Fixed Moments of Impulses and Its Solutions

   • Marat Akhmet

   Pages 7-24

4. Stability and Periodic Solutions of Systems with Fixed Moments of Impulses

   • Marat Akhmet

   Pages 25-30

5. Basics of Linear Systems

   • Marat Akhmet

   Pages 31-54

6. Nonautonomous Systems with Variable Moments of Impulses

   • Marat Akhmet

   Pages 55-80

7. Differentiability Properties of Nonautonomous Systems

   • Marat Akhmet

   Pages 81-98

8. Periodic Solutions of Nonlinear Systems

   • Marat Akhmet

   Pages 99-111

9. Discontinuous Dynamical Systems

   • Marat Akhmet

   Pages 113-137

10. Perturbations and Hopf Bifurcation of a Discontinuous Limit Cycle

    • Marat Akhmet

    Pages 139-154

11. Chaos and Shadowing

    • Marat Akhmet

    Pages 155-165

12. Back Matter

    Pages 167-176

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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.

• bifurcation
• biology
• computer
• computer science
• differential equation
• dynamical systems
• equation
• function
• functions
• mathematics
• online
• perturbation theory
• stability
• techniques
• variable
• ordinary differential equations
• partial differential equations

• Dept. Mathematics, Middle East Technical University (METU), Ankara, Turkey

  Marat Akhmet

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