Concept

Phase plane

Related lectures (32)

Mathematical Modeling in Chemistry and Biology

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

Canonical Transformations: Phase Portraits and Action Variables

Explores canonical transformations, phase portraits, and action variables in Hamiltonian systems and harmonic oscillators.

Bistability in Genetic Networks

Explores bistability in genetic networks, analyzing fixed points and stability, phase portraits, and experimental implementation.

Phase Plane Analysis

Covers the Phase Plane Analysis of 2-dimensional neuron models, focusing on nullclines and fixed points.

Bistability in Cell Cycle

Explores bistability in the cell cycle, emphasizing positive feedback mechanisms and abrupt response transformations.

Linear Systems in 2D: Stability

Explores stability in linear 2D systems, covering fixed points, vector fields, and phase portraits.

Phase Plane Analysis: Limit Cycles

Discusses limit cycles, equilibrium points, arbitrary curves, abstract plane, and numbering of points.

Non-linear Systems in 2D: Predator-Prey Models

Covers non-linear systems in 2D, focusing on predator-prey models and stability analysis of fixed points.

Hamilton-Jacobi Equations: Phase Portrait

Explores Hamilton-Jacobi equations, phase portrait, and period calculation using action-angle variables for system trajectories.

Stability Analysis: Linear Systems

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

Nonlinear Systems: Phase Portrait Analysis

Explores nonlinear systems through phase portraits in 2D, focusing on vector fields, isoclines, and trajectories.

Genetic Toggle Switch: Synthetic Biology Example

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

Hamilton-Jacobi Equation: Phase Portrait Analysis

Explores the Hamilton-Jacobi equation and phase portrait analysis in one-dimensional systems, emphasizing the relationship between variables and system evolution.

Phase Plane Analysis

Covers the analysis of phase planes for linear systems and the Poincaré-Bendixson theorem.

Reduction of Hodgkin-Huxley to 2D

Explores reducing the Hodgkin-Huxley model to a two-dimensional neuron model.

Phase Portraits and Predator-Prey Models

Explores phase portraits in 2D systems and the dynamics of predator-prey models.

Van der Pol Oscillator

Explores the Van der Pol oscillator, its dynamic equations, and phase plane representation.

Non-linear Control: Lyapunov Method

Covers exercises on the Lyapunov method in non-linear control systems, focusing on stability analysis and Lyapunov functions.

Genetic Circuits and Mechanical Analogies

Explores genetic circuits, negative feedback, and mechanical analogies for spatial problems, including cell coupling and mRNA regulation.

Analysis of a 2D neuron model: Constant input

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