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1 | (18) |
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2.1 A Geometric Way of Thinking |
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1 | (1) |
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2.2 Fixed Points and Stability |
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2 | (5) |
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7 | (2) |
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2.4 Linear Stability Analysis |
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9 | (2) |
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2.5 Existence and Uniqueness |
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11 | (2) |
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2.6 Impossibility of Oscillations |
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13 | (1) |
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13 | (1) |
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2.8 Solving Equations on the Computer |
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14 | (5) |
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19 | (46) |
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3.1 Saddle-Node Bifurcation |
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19 | (8) |
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3.2 Transcritical Bifurcation |
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27 | (4) |
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31 | (2) |
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3.4 Pitchfork Bifurcation |
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33 | (10) |
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3.5 Overdamped Bead on a Rotating Hoop |
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43 | (2) |
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3.6 Imperfect Bifurcations and Catastrophes |
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45 | (10) |
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55 | (10) |
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65 | (22) |
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4.1 Examples and Definitions |
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65 | (1) |
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66 | (1) |
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4.3 Nonuniform Oscillator |
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67 | (8) |
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75 | (2) |
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77 | (3) |
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4.6 Superconducting Josephson Junctions |
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80 | (7) |
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87 | (16) |
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5.1 Definitions and Examples |
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87 | (5) |
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5.2 Classification of Linear Systems |
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92 | (9) |
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101 | (2) |
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103 | (70) |
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103 | (6) |
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6.2 Existence, Uniqueness, and Topological Consequences |
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109 | (1) |
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6.3 Fixed Points and Linearization |
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110 | (7) |
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117 | (12) |
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129 | (16) |
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145 | (15) |
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160 | (4) |
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164 | (9) |
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173 | (46) |
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173 | (6) |
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7.2 Ruling Out Closed Orbits |
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179 | (9) |
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7.3 Poincare-Bendixson Theorem |
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188 | (9) |
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197 | (1) |
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7.5 Relaxation Oscillations |
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198 | (5) |
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7.6 Weakly Nonlinear Oscillators |
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203 | (16) |
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219 | (54) |
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8.1 Saddle-Node, Transcritical, and Pitchfork Bifurcations |
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219 | (7) |
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226 | (11) |
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8.3 Oscillating Chemical Reactions |
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237 | (4) |
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8.4 Global Bifurcations of Cycles |
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241 | (7) |
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8.5 Hysteresis in the Driven Pendulum and Josephson Junction |
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248 | (5) |
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8.6 Coupled Oscillators and Quasiperiodicity |
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253 | (14) |
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267 | (6) |
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273 | (34) |
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273 | (3) |
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9.2 Simple Properties of the Lorenz Equations |
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276 | (3) |
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9.3 Chaos on a Strange Attractor |
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279 | (13) |
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292 | (1) |
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9.5 Exploring Parameter Space |
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292 | (11) |
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9.6 Using Chaos to Send Secret Messages |
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303 | (4) |
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307 | (52) |
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10.1 Fixed Points and Cobwebs |
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307 | (11) |
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10.2 Logistic Map: Numerics |
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318 | (5) |
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10.3 Logistic Map: Analysis |
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323 | (8) |
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331 | (8) |
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339 | (3) |
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10.6 Universality and Experiments |
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342 | (10) |
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352 | (7) |
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359 | (12) |
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11.1 Countable and Uncountable Sets |
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359 | (1) |
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360 | (2) |
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11.3 Dimension of Self-Similar Fractals |
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362 | (4) |
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366 | (3) |
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11.5 Pointwise and Correlation Dimensions |
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369 | (2) |
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371 | |
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12.1 The Simplest Examples |
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371 | (10) |
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381 | (6) |
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387 | (2) |
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12.4 Chemical Chaos and Attractor Reconstruction |
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389 | (2) |
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12.5 Forced Double-Well Oscillator |
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391 | |
