Genetic Toggle Switch: Synthetic Biology Example

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

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

Covers the stability of discrete time periodic solutions and their properties.

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

Covers the convergence of fixed point methods for nonlinear equations, including global and local convergence theorems and the order of convergence.

Explores scaling and renormalization in statistical mechanics, emphasizing critical points and invariant properties.

Covers mathematical modeling in chemistry and biology, including chemical reactions, enzymatic kinetics, and population dynamics.

Explores the Banach Fixed Point Theorem, showing the uniqueness of fixed points in contraction mappings.

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

Explores the behavior of a 2D neuron model with constant input.