BIO-341: Dynamical systems in biology

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Lectures in this course (33)

Kuramoto Model: Phase Synchronization and Critical Coupling

Explores the Kuramoto model, discussing phase synchronization and critical coupling in oscillator populations.

Limit Cycles and Excitable Systems

Explores limit cycles, excitable systems, positive feedback, and phase locking in human circadian rhythms.

Circadian and Cell Cycle Dynamics: Coupling and Synchronization

Explores the synchronization and coupling of circadian and cell cycles, focusing on dynamics, predictions, and organ-specific time.

Limit Cycle Oscillators: Stability and Excitability

Explores limit cycle oscillators, stability, excitability, feedbacks, and fixed points in 2D phase portraits.

Entrainment and Synchronization of Oscillators

Explores entrainment and synchronization of oscillators, focusing on the Kuramoto model and resonance phenomena in human circadian rhythms.

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.

Synchronization in Kuramoto Model

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

Morphogen Gradients: Development and Patterns

Delves into morphogen gradients, logistic growth, and pattern formation in biological systems.

Kuramoto Model: Generalized Overview

Provides an overview of the generalized Kuramoto model, including natural frequencies, all-to-all coupling, bifurcation diagrams, and diffusion systems.

Diffusion Equation: Gaussian Solutions

Explores Gaussian solutions for the diffusion equation, ecological models, and morphogen gradients in biological systems.

Diffusion and Logistic Growth

Explores diffusion, logistic growth, genetic circuits, morphogen gradients, and wave propagation in biological systems.

Genetic Circuits and Mechanical Analogies

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

Propagation of Fronts in 1D

Explores the propagation of fronts in 1D systems using a mechanical analogy and bistable systems.

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