Transcritical Bifurcation: Theory and Applications

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

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

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

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

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

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

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

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

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

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