Author | Kaplan, Daniel. author |
---|---|
Title | Understanding Nonlinear Dynamics [electronic resource] / by Daniel Kaplan, Leon Glass |
Imprint | New York, NY : Springer New York : Imprint: Springer, 1995 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-0823-5 |
Descript | XX, 420 p. online resource |
1 Finite-Difference Equations -- 1.1 A Mythical Field -- 1.2 The Linear Finite-Difference Equation -- 1.3 Methods of Iteration -- 1.4 Nonlinear Finite-Difference Equations -- 1.5 Steady States and Their Stability -- 1.6 Cycles and Their Stability -- 1.7 Chaos -- 1.8 Quasiperiodicity -- 2 Boolean Networks and Cellular Automata -- 2.1 Elements and Networks -- 2.2 Boolean Variables, Functions, and Networks -- 2.3 Boolean Functions and Biochemistry -- 2.4 Random Boolean Networks -- 2.5 Cellular Automata -- 2.6 Advanced Topic: Evolution and Computation -- 3 Self-Similarity and Fractal Geometry -- 3.1 Describing a Tree -- 3.2 Fractals -- 3.3 Dimension -- 3.4 Statistical Self-Similarity -- 3.5 Fractals and Dynamics -- 4 One-Dimensional Differential Equations -- 4.1 Basic Definitions -- 4.2 Growth and Decay -- 4.3 Multiple Fixed Points -- 4.4 Geometrical Analysis of One-Dimensional Nonlinear Ordinary Differential Equations -- 4.5 Algebraic Analysis of Fixed Points -- 4.6 Differential Equations versus Finite-Difference Equations -- 4.7 Differential Equations with Inputs -- 4.8 Advanced Topic: Time Delays and Chaos -- 5 Two-Dimensional Differential Equations -- 5.1 The Harmonic Oscillator -- 5.2 Solutions, Trajectories, and Flows -- 5.3 The Two-Dimensional Linear Ordinary Differential Equation -- 5.4 Coupled First-Order Linear Equations -- 5.5 The Phase Plane -- 5.6 Local Stability Analysis of Two-Dimensional, Nonlinear Differential Equations -- 5.7 Limit Cycles and the van der Pol Oscillator -- 5.8 Finding Solutions to Nonlinear Differential Equations -- 5.9 Advanced Topic: Dynamics in Three or More Dimensions -- 5.10 Advanced Topic: Poincarรฉ Index Theorem -- 6 Time-Series Analysis -- 6.1 Starting with Data -- 6.2 Dynamics, Measurements, and Noise -- 6.3 The Mean and Standard Deviation -- 6.4 Linear Correlations -- 6.5 Power Spectrum Analysis -- 6.6 Nonlinear Dynamics and Data Analysis -- 6.7 Characterizing Chaos -- 6.8 Detecting Chaos and Nonlinearity -- 6.9 Algorithms and Answers -- Appendix A A Multi-Functional Appendix -- A.1 The Straight Line -- A.2 The Quadratic Function -- A.3 The Cubic and Higher-Order Polynomials -- A.4 The Exponential Function -- A.5 Sigmoidal Functions -- A.6 The Sine and Cosine Functions -- A.7 The Gaussian (or โNormalโ) Distribution -- A.8 The Ellipse -- A.9 The Hyperbola -- Exercises -- Appendix B A Note on Computer Notation -- Solutions to Selected Exercises