Lectures related to Nonlinear Dynamics and Chaos

Equilibrium Points and Bifurcations

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

Nonlinear Dynamics and Chaos

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

Dynamical Systems: Maps and Stability

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

Nonlinear Dynamics and Chaos

Explores logistic maps, bifurcations, equilibrium points, and periodic orbits in nonlinear dynamics and chaos.

Nonlinear Dynamics: Homoclinic Orbits and Bifurcations

Delves into homoclinic orbits, bifurcations, and limit cycles in nonlinear dynamics.

Bifurcations: Flip and Andronov-Hopf

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

Introduction to Quantum Chaos

Covers the introduction to Quantum Chaos, classical chaos, sensitivity to initial conditions, ergodicity, and Lyapunov exponents.

Dynamical Systems for Engineers

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

Dynamical System Theory: Bifurcations

Covers the topic of bifurcations in dynamical system theory, focusing on the pitchfork bifurcation.

Bifurcations: Introduction

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

Nonlinear Dynamics: Bifurcations and Stability

Explores nonlinear dynamics, bifurcations, stability, weakly nonlinear systems, saturation, Hopf bifurcation, and global stability analysis.

Special Types of Systems: Limit Cycles

Covers special types of systems, focusing on gradient systems and limit cycles, discussing equilibrium points, stability, and chaotic behavior.

Bifurcation and fractals in complex dynamical systems

Explores bifurcation, fractals, Julia sets, Mandelbrot set, and self-similarity in complex dynamical systems.

Fractional Susceptibility in Quadratic Dynamics

Explores the fractional susceptibility function in quadratic dynamical systems, highlighting its significance and the associated paradoxes in parameter dependence.

Transcritical Bifurcations: Understanding Dynamical Systems

Explores transcritical bifurcations and the dynamics near critical points.

Nonlinear Dynamics: Stability and Chaos

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

Introduction to Dynamical System

Introduces dynamical systems, equilibrium points, stability, vector fields, phase plots, and Lyapunov stability.

Attractors and Stability

Explores attractors and their stability in dynamical systems, including fixed points, periodic orbits, and chaotic attractors.

Limit Cycles in Biological Systems

Explores the concept of limit cycles in biological systems and their significance in understanding system dynamics.

Stellar Orbits: Integrals of Motion and Phase Space Visualization

Covers integrals of motion and surfaces of section in stellar dynamics.