Lectures related to Limit cycle

Shell Components in Meromorphic Parameter Spaces

Explores shell components in transcendental parameter planes and attracting cycles.

Mathematical Analysis of Genetic Circuits

Explores the mathematical analysis of genetic circuits and the implementation of synthetic plasmids in E. coli, focusing on the concept of limit cycle oscillators.

1st Harmonic: Stability and Adaptation

Covers stability, adaptation, Nyquist criterion, and predicting limit cycle existence.

Phase Plane Analysis

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

Special Types of Systems: Limit Cycles

Covers special types of systems, focusing on gradient systems and limit cycles, discussing equilibrium points, stability, and chaotic behavior.

Limit Cycles in Biological Systems

Explores the concept of limit cycles in biological systems and their significance in understanding system dynamics.

Genetic Toggle Switch: Bistability and Oscillations

Explores the genetic toggle switch, bistability, oscillations, and applications in gene therapy and biotechnology.

Nonlinear Dynamics: Homoclinic Orbits and Bifurcations

Delves into homoclinic orbits, bifurcations, and limit cycles in nonlinear dynamics.

Optomechanical Dynamics: Insights & Simulations

Explores nonlinear dynamics in optomechanical systems, covering instability, limit cycles, synchronization, chaos, and simulations.

Fourier Series and Harmonics

Covers Fourier series, harmonic decomposition, and limit cycle prediction in dynamic systems.

Beyond equilibrium: A dynamical systems approach to learning in games

Delves into learning dynamics in games, exploring chaos, limit cycles, and the interplay between convergence and chaos.

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 Cycles and Excitable Systems

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

Phase Plane Analysis: Limit Cycles

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

Fixed Points and Stability

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

Phase Plan and 1st Harmonic Method

Covers phase plan representation, limit cycles, topological index, and the first harmonic method.

Nonlinear Dynamics and Chaos

Covers bifurcations, long-term dynamics, logistic map, universality, and correspondence between different maps.

Small Scale Stability: Gradient Systems

Covers small scale stability in gradient systems, focusing on trajectory properties and equilibrium point attraction.

Limit Cycle Oscillators: Stability and Excitability

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

Algebraic Topology and Differential Geometry

Explores algebraic topology and differential geometry in understanding robot dynamics and global behavior.