Nonlinear Systems: Phase Portrait Analysis

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Covers the formalism and bases of dynamic systems, including differential equations and non-linear systems.

Covers the topic of nonlinear equations and the fixed point method.

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

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

Explores the Kuramoto model for synchronization in phase oscillators and discusses stability criteria and critical coupling values.

Explores fixed points and their stability in dynamic systems, emphasizing linear stability analysis.

Explores the analysis of phase portraits in 2D systems and the impact of parameter values on system dynamics.

Explores modeling gene expression, fixed points analysis, and stability in biological systems.

Explores the Newton method for non-linear equations, discussing convergence criteria and stopping conditions.

Covers the construction of a genetic toggle switch in Escherichia coli, a key example of synthetic biology.