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Transcritical Bifurcation: Theory and Applications
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Related lectures (32)
Dynamical Systems: Maps and Stability
Explores one-dimensional maps, periodic solutions, and bifurcations in dynamical systems.
Introduction to Dynamical System
Introduces dynamical systems, equilibrium points, stability, vector fields, phase plots, and Lyapunov stability.
Dynamical Systems: Equilibrium Points and Stability
Covers dynamical systems, equilibrium points, stability analysis, and phase plots using examples like the pendulum system.
Chaos and Lyapunov Exponents: Analyzing Predictability
Covers Lyapunov exponents, chaos measurement, and perturbation analysis in dynamical systems.
Chaos Theory: Turbulence and Double Pendulum
Delves into Chaos Theory, exploring chaotic systems, sensitivity to initial conditions, and the dynamics of the double pendulum.
Chaos Theory: Maps and Lyapunov Exponents
Explores chaotic maps, fix points, stability, and Lyapunov exponents in discrete systems, emphasizing their role in determining chaos.
Chaos Theory: Logistic Map and Periodic Orbits
Explores Chaos Theory, focusing on the logistic map, periodic orbits, and stability conditions.
Equilibrium Points and Bifurcations
Introduces equilibrium points and bifurcations in differential equations, discussing their stability and relevance in various contexts.
Chaos Theory: Discrete Dynamical Systems
Explores Chaos Theory through Discrete Dynamical Systems and the Arnold's Cat Map.
Dynamic Systems: Course Review
Covers dynamic systems, trajectories, growth models, stability of fixed points, and linearization of models.
Linear Systems in 2D: Stability
Explores stability in linear 2D systems, covering fixed points, vector fields, and phase portraits.
Nonlinear Dynamics: Stability and Chaos
Explores fixed point stability, Lyapunov functions, Lotka-Volterra models, and nonlinear dynamics in complex systems.
Nonlinear Dynamics and Chaos
Covers bifurcations, long-term dynamics, logistic map, universality, and correspondence between different maps.
Harmonic Responses to Non-Harmonic Signals
Covers the harmonic responses of systems to non-harmonic signals.
Nonlinear Dynamics and Chaos
Explores logistic maps, bifurcations, equilibrium points, and periodic orbits in nonlinear dynamics and chaos.
Chaos Theory: Chaotic Maps and Logistic Map
Explores chaotic maps, fix points, periodic orbits, and intermittent chaos.
Stability: Poles, Zeros, and Control
Covers stability, poles, zeros, and control in dynamic systems, emphasizing the importance of observability.
Stability Analysis: Linear Systems
Explores stability analysis in linear systems, emphasizing eigenvalues, eigenvectors, and stable manifolds.
Fractional Susceptibility in Quadratic Dynamics
Explores the fractional susceptibility function in quadratic dynamical systems, highlighting its significance and the associated paradoxes in parameter dependence.
Dynamic Systems: Formalism and Bases
Covers the formalism and bases of dynamic systems, including differential equations and non-linear systems.
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