A Visual Approach to Nonlinear Dynamics

A Visual Approach to Nonlinear Dynamics

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A Visual Approach to Nonlinear Dynamics: Unit 4: Lorenz Model • Fixed Points

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A Visual Approach to Nonlinear Dynamics: Unit 4: Lorenz Model • Fixed Points

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A Visual Approach to Nonlinear Dynamics

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  1. 1 A Visual Approach to Nonlinear Dynamics: Unit 1: Introduction • What is a Dynamical System?
  2. 2 A Visual Approach to Nonlinear Dynamics: Unit 1: Introduction • Types of Dynamical Systems
  3. 3 A Visual Approach to Nonlinear Dynamics: Unit 1: 1d Systems • Geometric Approach
  4. 4 A Visual Approach to Nonlinear Dynamics: Unit 1: 1d Systems • Classification of Fixed Points
  5. 5 A Visual Approach to Nonlinear Dynamics: Unit 1: 1d Systems • Local analysis at Fixed Points Part 1
  6. 6 A Visual Approach to Nonlinear Dynamics: Unit 1: 1d Systems • Local analysis at Fixed Points Part 2
  7. 7 A Visual Approach to Nonlinear Dynamics: Unit 1: 1d Systems • Algebraic vs. Geometric Approach
  8. 8 A Visual Approach to Nonlinear Dynamics: Unit 1: 1d Systems • Bifurcations in 1d
  9. 9 A Visual Approach to Nonlinear Dynamics: Unit 1: 1d Systems • Saddle Node Bifurcation
  10. 10 A Visual Approach to Nonlinear Dynamics: Unit 1: 1d Systems • Transcritical Bifurcation
  11. 11 A Visual Approach to Nonlinear Dynamics: Unit 1: 1d Systems • Subcritical Pitchfork Bifurcation
  12. 12 A Visual Approach to Nonlinear Dynamics: Unit 1: 1d Systems • Supercritical Pitchfork Bifurcation
  13. 13 A Visual Approach to Nonlinear Dynamics: Unit 1: 1d Systems • Catastrophes Part 1
  14. 14 A Visual Approach to Nonlinear Dynamics: Unit 1: 1d Systems • Catastrophes Part 2
  15. 15 A Visual Approach to Nonlinear Dynamics: Unit 1: 1d Systems • Catastrophes Part 3
  16. 16 A Visual Approach to Nonlinear Dynamics: Unit 1: Spruce Budworm Outbreak • Introduction
  17. 17 A Visual Approach to Nonlinear Dynamics: Unit 1: Spruce Budworm Outbreak • Dynamics
  18. 18 A Visual Approach to Nonlinear Dynamics: Unit 1: Periodic Systems • Firefly Synchronization Part 1
  19. 19 A Visual Approach to Nonlinear Dynamics: Unit 1: Periodic Systems • Firefly Synchronization Part 2
  20. 20 A Visual Approach to Nonlinear Dynamics: Unit 2: 2d Systems • Introduction
  21. 21 A Visual Approach to Nonlinear Dynamics: Unit 2: Linearized Analysis • Informal Introduction
  22. 22 A Visual Approach to Nonlinear Dynamics: Unit 2: Linearized Analysis • Example 1
  23. 23 A Visual Approach to Nonlinear Dynamics: Unit 2: Linearized Analysis • Example 2
  24. 24 A Visual Approach to Nonlinear Dynamics: Unit 2: Linearized Analysis • General Linear Analysis
  25. 25 A Visual Approach to Nonlinear Dynamics: Unit 2: Linearized Analysis • Types of Fixed Points
  26. 26 A Visual Approach to Nonlinear Dynamics: Unit 2: Linearized Analysis • Graph of Fixed Points
  27. 27 A Visual Approach to Nonlinear Dynamics: Unit 2: Competition-Mutualism • Two Interacting Species
  28. 28 A Visual Approach to Nonlinear Dynamics: Unit 2: Competition-Mutualism • Nullclines
  29. 29 A Visual Approach to Nonlinear Dynamics: Unit 2: Competition-Mutualism • Linearized Transformation
  30. 30 A Visual Approach to Nonlinear Dynamics: Unit 2: Competition-Mutualism • Summary
  31. 31 A Visual Approach to Nonlinear Dynamics: Unit 2: Two Species Model • Asymmetric Interaction Part 1
  32. 32 A Visual Approach to Nonlinear Dynamics: Unit 2: Two Species Model • Asymmetric Interaction Part 2
  33. 33 A Visual Approach to Nonlinear Dynamics: Unit 2: Two Species Model • Prey-Predator Interaction
  34. 34 A Visual Approach to Nonlinear Dynamics: Unit 2: Cycles and Bifurcations • Features 2d Trajectories
  35. 35 A Visual Approach to Nonlinear Dynamics: Unit 2: Cycles and Bifurcations • Example of Limit Cycle
  36. 36 A Visual Approach to Nonlinear Dynamics: Unit 2: Cycles and Bifurcations • Glycolysis Model
  37. 37 A Visual Approach to Nonlinear Dynamics: Unit 2: Cycles and Bifurcations • Glycolysis Model Part 2
  38. 38 A Visual Approach to Nonlinear Dynamics: Unit 2: van der Pol Oscillator Part 1
  39. 39 A Visual Approach to Nonlinear Dynamics: Unit 2: van der Pol Oscillator Part 2
  40. 40 A Visual Approach to Nonlinear Dynamics: Unit 2: Cycles and Bifurcations • Bifurcations in 2d
  41. 41 A Visual Approach to Nonlinear Dynamics: Unit 2: Cycles and Bifurcations • Types of 2d Bifurcations
  42. 42 A Visual Approach to Nonlinear Dynamics: Unit 2: Super Critical Hopf Bifurcation
  43. 43 A Visual Approach to Nonlinear Dynamics: Unit 2: Cycles and Bifurcations • Hopf Bifurcation
  44. 44 A Visual Approach to Nonlinear Dynamics: Unit 3: General Features • Motivation
  45. 45 A Visual Approach to Nonlinear Dynamics: Unit 3: Linear vs. Nonlinear & Continuous vs. Noncontinuous
  46. 46 A Visual Approach to Nonlinear Dynamics: Unit 3: Logistic Map • Basic Features of Iteration Pt. 1
  47. 47 A Visual Approach to Nonlinear Dynamics: Unit 3: Logistic Map • Basic Features of Iteration Pt. 2
  48. 48 A Visual Approach to Nonlinear Dynamics: Unit 3: Logistic Map • FP Analysis and the 1st Bifurcation
  49. 49 A Visual Approach to Nonlinear Dynamics: Unit 3: Logistic Map • Fixed Point Analysis for 2 Cycle
  50. 50 A Visual Approach to Nonlinear Dynamics: Unit 3: Logistic Map • Phenomenology of Bifurcations
  51. 51 A Visual Approach to Nonlinear Dynamics: Unit 3: Logistic Map • 3 Cycle Dynamics
  52. 52 A Visual Approach to Nonlinear Dynamics: Unit 3: Chaos and Lyapunov Exponents
  53. 53 A Visual Approach to Nonlinear Dynamics: Unit 3: 1d Linear Delay Equation • Delay Dynamical Systems
  54. 54 A Visual Approach to Nonlinear Dynamics: Unit 3: 1d Linear Delay Equation • Stability Analysis Pt 1
  55. 55 A Visual Approach to Nonlinear Dynamics: Unit 3: 1d Linear Delay Equation • Stability Analysis Pt 2
  56. 56 A Visual Approach to Nonlinear Dynamics: Unit 4: 3d Systems • General Discussion
  57. 57 A Visual Approach to Nonlinear Dynamics: Unit 4: 3-Species Competition • Introduction to 2-Species
  58. 58 A Visual Approach to Nonlinear Dynamics: Unit 4: 3-Species Competition • Introduction to 3-Species
  59. 59 A Visual Approach to Nonlinear Dynamics: Unit 4: 3-Species Competition • Stability of Fixed Points 1
  60. 60 A Visual Approach to Nonlinear Dynamics: Unit 4: 3-Species Competition • Stability of Fixed Points 2
  61. 61 A Visual Approach to Nonlinear Dynamics: Unit 4: 3-Species Competition • Special Case of α + β = 2
  62. 62 A Visual Approach to Nonlinear Dynamics: Unit 4: 3-Species Competition • Summary
  63. 63 A Visual Approach to Nonlinear Dynamics: Unit 4: 3-Species Competition • Non-Periodic Regime
  64. 64 A Visual Approach to Nonlinear Dynamics: Unit 4: Driven Damped Pendulum • Introduction
  65. 65 A Visual Approach to Nonlinear Dynamics: Unit 4: Driven Damped Pendulum • Small Forcing Limit
  66. 66 A Visual Approach to Nonlinear Dynamics: Unit 4: Driven Damped Pendulum • Nonlinear Regime
  67. 67 A Visual Approach to Nonlinear Dynamics: Unit 4: Lorenz Model • Motivation
  68. 68 A Visual Approach to Nonlinear Dynamics: Unit 4: Lorenz Model • Basic Properties Lorenz Equation
  69. 69 A Visual Approach to Nonlinear Dynamics: Unit 4: Lorenz Model • Fixed Points
  70. 70 A Visual Approach to Nonlinear Dynamics: Unit 4: Lorenz Model • Stability of Fixed Points
  71. 71 A Visual Approach to Nonlinear Dynamics: Unit 4: Lorenz Model • Lyapunov Function
  72. 72 A Visual Approach to Nonlinear Dynamics: Unit 4: Lorenz Model • Trajectories in Chaotic Regime
  73. 73 A Visual Approach to Nonlinear Dynamics: Unit 4: Lorenz Model • Lorenz Map

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