Lectures related to Nonlinear Dynamical Systems: Key Concepts

Introduction to Dynamical System Theory for Engineers

Covers trajectory, solution, and orbit of dynamical systems for engineers.

Nonlinear Dynamics: Homoclinic Orbits and Bifurcations

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

Introduces dynamical systems, equilibrium points, stability, vector fields, phase plots, and Lyapunov stability.

Covers chaotic behavior in complex systems, with applications in various fields and a historical overview of major developments in chaos theory.

Dynamical Systems for Engineers

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

Chaos Theory: Turbulence and Double Pendulum

Delves into Chaos Theory, exploring chaotic systems, sensitivity to initial conditions, and the dynamics of the double pendulum.

Functions Composition: Continuity & Elements

Covers the composition of functions, continuity, and elementary functions, explaining the concept of continuity and the construction of elementary functions.

Discrete Systems Theory

Covers difference equations, dynamic systems, linearity, and impulse response in discrete systems.

Chaos and Lyapunov Exponents: Analyzing Predictability

Covers Lyapunov exponents, chaos measurement, and perturbation analysis in dynamical systems.

Dynamical Systems: Equilibrium Points and Stability

Covers dynamical systems, equilibrium points, stability analysis, and phase plots using examples like the pendulum system.

Dynamical Systems: Maps and Stability

Explores one-dimensional maps, periodic solutions, and bifurcations in dynamical systems.

Linear Response in High-Dimensional Systems

Explores linear response in high-dimensional systems, covering theory, practice, and implications of non-hyperbolicity and inhomogeneous subsystems.

State-space Modeling

Introduces the state-space approach to modeling dynamical systems and its utility for high-speed solution of differential equations and computer algorithms.

Convolution and Laplace Transform

Explores control of dynamic systems, impulse response, Laplace transform, and Fourier transform for solving differential equations.

Shell Components in Meromorphic Parameter Spaces

Explores shell components in transcendental parameter planes and attracting cycles.

Developpements limités

Explains the definition and uniqueness of developments limites for continuous functions on open intervals.

Dynamics of Discrete Systems

Covers the dynamics of discrete systems and the concept of orbits in Riemann varieties.

Mechanics: Introduction and Calculus

Introduces mechanics, differential and vector calculus, and historical perspectives from Aristotle to Newton.

Learning Chemical Reaction Networks

Explores sparse learning of chemical reaction networks from trajectory data using data-based methods and learning approaches.

Continuous Functions: Definition

Explains the definition of continuous functions and isolated points.