Nonlinear Dynamical Systems: Key Concepts

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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.