Watch Current Video List All Videos ✓ 1d Systems ✓ Introduction to Dynamical Systems ✓ What is Dynamical System? ✓ Types of Dynamical Systems ✓ Introduction to 1d Systems ✓ Geometric Approach ✓ Classification of Fixed Points ✓ Local analysis at Fixed Points (linear and nonlinear) Part 1 ✓ Local analysis at Fixed Points (linear and nonlinear) Part 2 ✓ Algebraic vs. Geometric Approach ✓ Bifurcations in 1d Systems ✓ Bifurcations in 1d ✓ Saddle Node Bifurcation (2 FPs born in a vacuum) ✓ Transcritical Bifurcation ✓ Subcritical Pitchfork Bifurcation (stable FP becomes unstable) ✓ Supercritical Pitchfork Bifurcation ✓ Catastrophes in 1d Systems ✓ Catastrophes ✓ Stability Diagram ✓ Fixed Point Locations ✓ Spruce Budworm Outbreak ✓ Introduction ✓ Dynamics ✓ Periodic Systems ✓ Firefly Synchronization Part 1 ✓ Firefly Synchronization Part 2 ✓ 2d Systems ✓ Introduction to 2d Systems ✓ Introduction ✓ Linearized Analysis in 2d Systems ✓ Informal Introduction to Linearized Analysis ✓ Example 1 ✓ Example 2 ✓ General Linear Analysis ✓ Types of Fixed Points ✓ Graphical Representation of Fixed Points ✓ Two Species Model ✓ Competition-Mutualism • Two Interacting Species ✓ Competition-Mutualism • Nullclines ✓ Competition-Mutualism • Linearized Transformation ✓ Competition-Mutualism • Summary ✓ Asymmetric Interaction Part 1 ✓ Asymmetric Interaction Part 2 ✓ Prey-Predator Interaction ✓ Cycles and Bifurcation ✓ New Features of 2d Trajectories ✓ Example of Limit Cycle • Rotation ✓ Glycolysis Model Part 1 ✓ Glycolysis Model Part 2 ✓ van der Pol Oscillator Part 1 ✓ van der Pol Oscillator Part 2 ✓ Bifurcations in 2d ✓ Super Critical Hopf Bifurcation ✓ Hopf Bifurcation in Glycolysis Reaction ✓ Discrete and Delay Systems ✓ Introduction to Discrete and Delay Systems ✓ General Features • Motivation ✓ Linear vs. Non-linear & Continuous vs. Non-continuous ✓ Logistic Map ✓ Basic Features of Iteration Pt. 1 ✓ Basic Features of Iteration Pt. 2 ✓ Fixed Point Analysis and the First Bifurcation ✓ Fixed Point Analysis for 2-Cycle ✓ Phenomenology of Bifurcations ✓ 3-Cycle Dynamics ✓ Chaos in Dynamical Systems ✓ Chaos and Lyapunov Exponents ✓ 1d Linear Delay Equation ✓ Delay in Dynamical Systems ✓ Stability Analysis Part 1 ✓ Stability Analysis Part 2 ✓ 3d Systems & Beyond ✓ Introduction to >2d Systems ✓ General Discussion ✓ Three Species Competition Model ✓ Introduction to 2-Species ✓ Introduction to 3-Species ✓ Fixed Points and Their Stability Part 1 ✓ Fixed Points and Their Stability Part 2 ✓ Special Case of α + β = 2 ✓ Summary ✓ Non-Periodic Regime ✓ Driven Damped Pendulum ✓ Introduction ✓ Small Forcing Limit ✓ Nonlinear Regime ✓ Lorenz Model ✓ Motivation ✓ Basic Properties of the Lorenz Equation ✓ Fixed Points ✓ Stability of Fixed Points ✓ Lyapunov Function ✓ Trajectories in Chaotic Regime ✓ Lorenz Map ✓ 1.1 Introduction to Dynamical Systems » What is Dynamical System?