We ek |
Date | Lec- ture |
Contents |
1 | 1231 |
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0102 | L01 |
outline overview; examples of the geometric approach |
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0104 | L02 | PART I. One dimensional flows
§2.1-2.3 one dimensional flow, fixed points, their stability, logistic equation |
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2 | 0107 | L03 | §2.4 stability analysis: by graph and by derivative |
0109 | L04 | demonstration of the software XPPAUT §2.5 the theorem on unique existence of solutions |
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0111 | L05 | §2.5 impossibility of oscillation §2.6 potential §3.1 saddle-node bifurcation |
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3 | 0114 | L06 | §3.1 bifurcation diagram, normal form |
0116 | L07 | §3.2 transcritical bifurcation |
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0118 | L08 | §3.4 pitchfork bifurcation: supercritical and
subcritical |
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4 | 0121 | L09 | §3.4 subcritical pitchfork bifurcation with
higher order damping term, jump and hysteresis |
0123 | L10 | §3.5 over-damped bead on a rotating vertical
hoop |
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0125 |
L11 | §3.6 imperfect bifurcation |
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5 | 0128 |
L12 | §3.6 imperfect bifurcation continued §3.7 insect outbreak |
0130 |
L13 | §3.7 insect outbreak continued PART II. Two dimensional flows Chapter 5 2D linear flows |
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0201 |
L14 | §5.2 classification of 2D linear flows
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6 | 0204 |
L15 | Chapter 6 2D nonlinear flows §6.3 fixed points and linearization |
0206 |
L16 |
§6.3 examples |
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0208 |
L17 | §6.4 competition models |
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7 | 0211 |
Family Day | |
0213 |
midterm exam |
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0215 |
L18 | §6.5 conservative systems, example: Newton's
equation |
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0218-0222 | |
midterm break | |
8 | 0225 |
L19 | §6.5 example: Hamiltonian systems §6.6 Reversible systems |
0227 |
L20 | §6.6 examples |
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0301 |
L21 | Chapter 7 Limit cycles §7.1 limit cycles, examples §7.2 nonexistence: gradient flows |
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9 | 0304 |
L22 | §7.2 nonexistence: Lyapunov functions, Dulac's
criterion |
0306 |
L23 | §7.2 examples of Dulac's
criterion §7.3 Poincare-Bendixson theorem |
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0308 |
L24 | §7.3 examples of Poincare-Bendixson theorem
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10 | 0311 |
L25 | §7.4 Lienard equation, Poincare map |
0313 |
L26 | §8.1 SN, TC and PF bifurcations for 2D systems §8.2 Introduction to Hopf bifurcation |
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0315 |
L27 | §8.2 Hopf bifurcation |
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11 | 0318 |
L28 | §8.2 one more example §8.3 Belousov-Zhabotinsky reaction: oscillating chemical reactions links: wikipedia, youtube video 1, youtube video 2 |
0320 |
L29 | §8.3 continued §8.7 Poincare map |
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0322 |
L30 | §8.7 continued |
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12 | 0325 |
L31 | §8.6 invariant tori, (optional:
an example
of an invariant torus)
§9.2 Lorenz equations |
0327 |
L32 | §9.2 Lorenz equations continued |
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0329 |
Good Friday | ||
13 |
0401 |
Easter Monday | |
0403 |
L33 |
§9.3 chaos and strange attractor §9.5 exploring the parameter space |
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0405 |
finish §9.5 and review |