Dynamical System Theory: Bifurcations

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Nonlinear Dynamics: Homoclinic Orbits and Bifurcations

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

Introduction to Dynamical System

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

Fractional Susceptibility in Quadratic Dynamics

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

Nonlinear Dynamics: Bifurcations and Stability

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

Fractional Response

Explores linear response in dynamical systems, emphasizing fractional derivatives and expanding unimodal maps.

Bifurcations: Fold Bifurcation

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

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.

Stellar Orbits: Integrals of Motion and Phase Space Visualization

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

Dynamical Systems: Equilibrium Points and Stability

Covers dynamical systems, equilibrium points, stability analysis, and phase plots using examples like the pendulum system.

Attractors and Stability

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