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Textbook Of Dynamic Systems
Paperback
General MathematicsGeneral Science
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ISBN13: 9798193680505
Publisher: Independently Published
Pages: 290
Weight: 1.49
Height: 0.61 Width: 8.50 Depth: 11.00
Language: English
Publisher: Independently Published
Pages: 290
Weight: 1.49
Height: 0.61 Width: 8.50 Depth: 11.00
Language: English
What makes a system settle into equilibrium, oscillate forever, suddenly change behavior-or become chaotic?TEXTBOOK OF DYNAMIC SYSTEMS gives you a rigorous but approachable path into the mathematics of systems that evolve over time. Rather than treating differential equations as formulas to solve mechanically, this book teaches you to see the geometry behind them: flows, phase portraits, equilibria, attractors, bifurcations, and the structures that determine long-term behavior.
Built for students, independent learners, engineers, and mathematically curious readers with a background in calculus and introductory linear algebra, this textbook develops intuition alongside precise mathematical reasoning.
Inside, you will learn to:
Inside, you will learn to:
- Analyze continuous and discrete dynamical systems using geometric and qualitative methods
- Classify equilibria through eigenvalues, eigenvectors, linearization, and stability theory
- Apply Lyapunov methods, nullclines, trapping regions, and phase-plane analysis
- Understand limit cycles and the Poincaré-Bendixson theorem
- Recognize saddle-node, transcritical, pitchfork, Hopf, and other bifurcations
- Explore the Lorenz system, strange attractors, Lyapunov exponents, fractals, and deterministic chaos
- Connect continuous flows with discrete maps, including logistic-map dynamics and symbolic methods
- Study Hamiltonian systems, structural stability, scientific applications, and practical numerical techniques
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