2 Flows on the Line; 2.1 A Geometric Way of Thinking; 2.2 Fixed Points and Stability; 2.3 Population Growth; 2.4 Linear Stability Analysis; 2.5 Existence and Uniqueness; 2.6 Impossibility of Oscillations; 2.7 Potentials; 2.8 Solving Equations on the Computer; 3 Bifurcations; 3.1 Saddle-Node Bifurcation; 3.2 Transcritical Bifurcation; 3.3 Laser Threshold; 3.4 Pitchfork Bifurcation; 3.5 Overdamped Bead on a Rotating Hoop; 3.6 Imperfect Bifurcations and Catastrophes; 3.7 Insect Outbreak; 4 Flows on the Circle; 4.1 Examples and Definitions.
10 One-Dimensional Maps10.1 Fixed Points and Cobwebs; 10.2 Logistic Map: Numerics; 10.3 Logistic Map: Analysis; 10.4 Periodic Windows; 10.5 Liapunov Exponent; 10.6 Universality and Experiments; 10.7 Renormalization; 11 Fractals; 11.1 Countable and Uncountable Sets; 11.2 Cantor Set; 11.3 Dimension of Self-Similar Fractals; 11.4 Box Dimension; 11.5 Pointwise and Correlation Dimensions; 12 Strange Attractors; 12.1 The Simplest Examples; 12.2 Hénon Map; 12.3 Rössler System; 12.4 Chemical Chaos and Attractor Reconstruction; 12.5 Forced Double-Well Oscillator.
4.2 Uniform Oscillator4.3 Nonuniform Oscillator; 4.4 Overdamped Pendulum; 4.5 Fireflies; 4.6 Superconducting Josephson Junctions; 5 Linear Systems; 5.1 Definitions and Examples; 5.2 Classification of Linear Systems; 5.3 Love Affairs; 6 Phase Plane; 6.1 Phase Portraits; 6.2 Existence, Uniqueness, and Topological Consequences; 6.3 Fixed Points and Linearization; 6.4 Rabbits versus Sheep; 6.5 Conservative Systems; 6.6 Reversible Systems; 6.7 Pendulum; 6.8 Index Theory; 7 Limit Cycles; 7.1 Examples; 7.2 Ruling Out Closed Orbits; 7.3 Poincaré-Bendixson Theorem; 7.4 Liénard Systems.
7.5 Relaxation Oscillations7.6 Weakly Nonlinear Oscillators; 8 Bifurcations Revisited; 8.1 Saddle-Node, Transcritical, and Pitchfork Bifurcations; 8.2 Hopf Bifurcations; 8.3 Oscillating Chemical Reactions; 8.4 Global Bifurcations of Cycles; 8.5 Hysteresis in the Driven Pendulum and Josephson Junction; 8.6 Coupled Oscillators and Quasiperiodicity; 8.7 Poincaré Maps; 9 Lorenz Equations; 9.1 A Chaotic Waterwheel; 9.2 Simple Properties of the Lorenz Equations; 9.3 Chaos on a Strange Attractor; 9.4 Lorenz Map; 9.5 Exploring Parameter Space; 9.6 Using Chaos to Send Secret Messages.
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This official Student Solutions Manual includes solutions to the odd-numbered exercises featured in the second edition of Steven Strogatz's classic text Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering. The textbook and accompanying Student Solutions Manual are aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. Complete with graphs and worked-out solutions, this manual demonstrates techniques for students to analyze differential equations, bifurcations, chaos, fractals, and other subjects Strogatz explores in his popular book.
Ingram Content Group
9780429972638
9780813350547
9781138329874
Nonlinear Dynamics and Chaos
Chaotic behavior in systems, Problems, exercises, etc.