Nonlinear Dynamics: Bifurcations and Stability

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Weakly Nonlinear Approach: Bifurcations and Amplitude Equations

Explores weakly nonlinear approach, bifurcations, amplitude equations, critical slowing, and nonlinearities in dynamical systems.

Introduction to Quantum Chaos

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

Limit Cycles in Biological Systems

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

Stellar Orbits: Stability and Resonances

Explores the stability of orbits, effective potential shape, and resonances in stellar dynamics.

Stability Analysis: Linear Systems

Explores stability analysis in linear systems, emphasizing eigenvalues, eigenvectors, and stable manifolds.

Transcritical Bifurcations: Understanding Dynamical Systems

Explores transcritical bifurcations and the dynamics near critical points.

Fractional Susceptibility in Quadratic Dynamics

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

Introduction to Dynamical System

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

Fractional Response

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

Weakly Nonlinear Analysis: Multiple Time Scale Expansion

Explores weakly nonlinear analysis through multiple time scale expansion, emphasizing the period of a gravitational pendulum and non-resonance conditions.