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Lecture
Small Scale Stability: Equilibrium Point
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Small Scale Stability: Equilibrium Point
Covers small scale stability at equilibrium points in dynamical systems for engineers.
Introduction to Dynamical System
Introduces dynamical systems, equilibrium points, stability, vector fields, phase plots, and Lyapunov stability.
Dynamical Systems: Equilibrium Points and Stability
Covers dynamical systems, equilibrium points, stability analysis, and phase plots using examples like the pendulum system.
Dynamical System Theory for Engineers: Large Scale Stability
Covers the concept of large scale stability in dynamical systems.
Dynamical System Theory for Engineers: Large Scale Stability
Explores large scale stability in dynamical systems, emphasizing non-increasing trajectories and strict decrease of a specific function.
Small Scale Stability: Solutions and Stability Analysis
Explores small scale stability, analyzing solutions' stability conditions locally and globally.
Bifurcations: Fold Bifurcation
Covers the concept of fold bifurcation in dynamical systems, focusing on the saddle-mode behavior.
Lyapunov Stability in Dynamical Systems
Covers Lyapunov stability in dynamical systems, focusing on global asymptotic stability and practical implementation through semidefinite programming.
Small Scale Stability: Gradient Systems
Explores small scale stability in gradient systems, analyzing trajectories and attractors in phase space.
Nonlinear Dynamics: Stability and Chaos
Explores fixed point stability, Lyapunov functions, Lotka-Volterra models, and nonlinear dynamics in complex systems.
