Lectures related to Phase portrait

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.

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.

Bistability in Cell Cycle

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

Hamilton-Jacobi Equations: Phase Portrait

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

Linear Systems in 2D: Stability

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

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.

Thermodynamic formalism for coarse expanding dynamical systems

Explores thermodynamic formalism for weakly coarse expanding dynamical systems, covering equilibrium states, visual metrics, and symbolic coding.

Genetic Circuits and Mechanical Analogies

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

Phase Portrait and Non-linear Systems

Covers phase portraits, eigenvalue decomposition, Jordan decomposition, and stable nodes in non-linear systems.

Phase Portraits and Predator-Prey Models

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

Dynamical Systems for Engineers

Covers the theoretical basis of linear and nonlinear dynamical systems for engineers.

Canonical Transformations in Hamiltonian Mechanics

Explores canonical transformations in Hamiltonian mechanics, emphasizing variable separation in the Hamilton-Jacobi equation.

Dynamics of Simple Pendulum and Lorenz Equations

Explores the dynamics of a simple pendulum and the intriguing Lorenz equations, highlighting sensitivity to initial conditions and the transition to chaos.

Analysis of Phase Portraits in 2D Systems

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

Conservation of Mechanical Energy

Explores the conservation of mechanical energy, equilibrium stability, and phase portraits.

Industrial Applications of Computer Modelling

Delves into computer modelling for industrial applications, emphasizing surfactant science and its practical deployment.