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Averaging for Nonlinear Dynamics with Applications and Numerical Bifurcations: Parametric and Autoparametric Systems, Hamiltonian Systems, Fpu Systems
Hardcover
Series: Applied Mathematical Sciences, Book 223
General MathematicsGeneral Science
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ISBN10: 3032127440
ISBN13: 9783032127440
Publisher: Springer
Published: Feb 8 2026
Pages: 276
Weight: 1.29
Height: 0.69 Width: 6.14 Depth: 9.21
Language: English
ISBN13: 9783032127440
Publisher: Springer
Published: Feb 8 2026
Pages: 276
Weight: 1.29
Height: 0.69 Width: 6.14 Depth: 9.21
Language: English
This book presents a comprehensive and practical survey of averaging methods for differential equations. Combining rigorous theory with applied perspectives, this book serves as both a study text and a reference for mathematicians and scientists in fields such as engineering, physics, and biology. Divided into two complementary parts, the book begins with Part I, the Toolbox of Averaging Theorems, providing clear definitions, theorem formulations, and foundational results. While mathematicians may be content with existence proofs and qualitative analyses, applied scientists require tools that link theory to real-world problems--an essential motivation for Part II.
Part II explores applications in physics and engineering, blending theory with practice and incorporating numerical bifurcation analysis using tools such as AUTO, Mathematica, and MatCont. Interspersed theoretical interludes provide the background necessary for understanding and applying these methods. Highlights include:
- Hamiltonian systems (Ch. 9), examining resonance phenomena in physics and engineering. Fermi-Pasta-Ulam chains (Ch. 10), extending fundamental theory. Parametric excitation (Ch. 11) and dissipation-induced instability (Ch. 13), showcasing classical but lesser-known engineering results. Coupled oscillators and chaos (Ch. 12), a detailed exploration of complex nonlinear dynamics. Diffusion and waves (Ch. 14), providing essential guidance while pointing to broader material for further study.
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