Lecture
Equilibrium Points and Bifurcations
In course
DEMO: laboris ad ex
Cupidatat ipsum veniam excepteur ullamco adipisicing ut qui anim consequat cupidatat dolor. Consequat nostrud aliqua amet aliquip do. Eiusmod aliqua esse esse exercitation excepteur velit elit sint labore deserunt. Sunt magna ex eiusmod fugiat ad do.
Description
This lecture covers the concept of equilibrium points in differential equations, where the derivative is zero, and introduces bifurcations, which are changes in the qualitative behavior of solutions. It explains how initial conditions correspond to fixed points and discusses the stability of these points. The lecture also delves into the logistic model, showing how it relates to complex life systems. Additionally, it explores saddle nodes and pitchfork bifurcations, illustrating how these phenomena occur in problems with symmetry. The instructor provides insights into the dynamics of nonlinear systems, chaos, and complex systems, highlighting the importance of understanding equilibrium points and bifurcations in various contexts.
Instructor
et consectetur
Aute ad aliqua cupidatat cupidatat consectetur laboris dolor excepteur aute ad officia aliquip cupidatat pariatur. Ullamco cupidatat commodo do aliquip nisi. Veniam non dolore aliquip cillum ad incididunt. In sit enim ipsum adipisicing occaecat est do labore fugiat. Magna aliquip nulla pariatur fugiat ut ullamco occaecat et ullamco eu do.
Official source
About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.
Ontological neighbourhood
Related lectures (44)
Introduction to Quantum Chaos
Covers the introduction to Quantum Chaos, classical chaos, sensitivity to initial conditions, ergodicity, and Lyapunov exponents.
Dynamical Systems: Maps and Stability
Explores one-dimensional maps, periodic solutions, and bifurcations in dynamical systems.
Nonlinear Dynamics and Chaos
Explores logistic maps, bifurcations, equilibrium points, and periodic orbits in nonlinear dynamics and chaos.
Physics Mini-Test: Trajectory Analysis
Explores the analysis of a ball's trajectory in contact with a beam, focusing on forces, angles, and motion equations.
Existence and Uniqueness of Solutions
Explores the existence and uniqueness of solutions for differential equations through local Lipschitz continuity and the Cauchy-Lipschitz theorem.