Lectures related to Transcritical Bifurcation: Theory and Applications

Explores one-dimensional maps, periodic solutions, and bifurcations in dynamical systems.

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.

Transcritical Bifurcation in Dynamical Systems

Explores transcritical bifurcation in dynamical systems, with a focus on SIS epidemics and their mathematical analysis.

Bifurcations: Fold Bifurcation

Covers the concept of fold bifurcation in dynamical systems, focusing on the saddle-mode behavior.

Bifurcations: Flip and Andronov-Hopf

Explores flip and Andronov-Hopf bifurcations, showing how systems change equilibrium points and stability.

Chaos and Lyapunov Exponents: Analyzing Predictability

Covers Lyapunov exponents, chaos measurement, and perturbation analysis in dynamical systems.

Chaos Theory: Turbulence and Double Pendulum

Delves into Chaos Theory, exploring chaotic systems, sensitivity to initial conditions, and the dynamics of the double pendulum.

Bifurcations: Introduction

Covers the introduction to bifurcations in dynamical systems, including examples and theorems.

Chaos Theory: Maps and Lyapunov Exponents

Explores chaotic maps, fix points, stability, and Lyapunov exponents in discrete systems, emphasizing their role in determining chaos.

Chaos Theory: Logistic Map and Periodic Orbits

Explores Chaos Theory, focusing on the logistic map, periodic orbits, and stability conditions.

Dynamical Systems for Engineers

Covers the theoretical basis of linear and nonlinear dynamical systems for engineers.

Eigenstate Thermalization Hypothesis

Explores the Eigenstate Thermalization Hypothesis in quantum systems, emphasizing the random matrix theory and the behavior of observables in thermal equilibrium.

Equilibrium Points and Bifurcations

Introduces equilibrium points and bifurcations in differential equations, discussing their stability and relevance in various contexts.

Chaos Theory: Discrete Dynamical Systems

Explores Chaos Theory through Discrete Dynamical Systems and the Arnold's Cat Map.

Dynamic Systems: Course Review

Covers dynamic systems, trajectories, growth models, stability of fixed points, and linearization of models.

Linear Systems in 2D: Stability

Explores stability in linear 2D systems, covering fixed points, vector fields, and phase portraits.

Nonlinear Dynamics: Stability and Chaos

Explores fixed point stability, Lyapunov functions, Lotka-Volterra models, and nonlinear dynamics in complex systems.

Nonlinear Dynamics and Chaos

Covers bifurcations, long-term dynamics, logistic map, universality, and correspondence between different maps.

Harmonic Responses to Non-Harmonic Signals

Covers the harmonic responses of systems to non-harmonic signals.