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Chaotic System
Dynamic system exhibiting extreme sensitivity to initial conditions, making its long-term behavior unpredictable despite deterministic laws. These systems exhibit aperiodic but bounded behavior, characterized by strange attractors in phase space.
Kohonen Maps
Unsupervised neural networks performing a non-linear projection of high-dimensional data onto a low-dimensional grid. Preserve the topology of data while allowing visualization and classification of complex structures.
Embedding Method
Non-linear analysis technique reconstructing phase space from a single time series through time delays. Allows estimation of quantities such as correlation dimension and Lyapunov exponents.
Lyapunov Exponents
Measures quantifying the rate of divergence or convergence of neighboring trajectories in the phase space of a dynamic system. A positive exponent indicates chaotic behavior and sensitivity to initial conditions.
Chaos Synchronization
Phenomenon where two or more coupled chaotic systems evolve toward identical trajectories despite their unpredictable nature. Applications in secure communications and non-linear signal processing.
Catastrophe Theory
Branch of mathematics studying discontinuities appearing in continuous systems under the influence of control parameters. Models abrupt transitions and qualitative changes in complex systems.
Fractal Dimension
Measure quantifying the geometric complexity of an object or set by its ability to fill space. Non-integer value characterizing the self-similarity and irregularity at different scales of complex structures.
Networks of Coupled Oscillators
Systems composed of interconnected periodic units exchanging information and capable of exhibiting collective synchronization phenomena. Model complex biological, neuronal, and physical processes.
Wavelet Transform
Mathematical tool that decomposes signals into time-localized frequency components, suitable for analyzing non-stationary signals. Particularly effective for detecting multiscale structures in complex data.
Non-Linear Support Vector Machines
Extension of SVMs that use kernel functions to project data into a higher-dimensional space where they become linearly separable. Capable of modeling complex decision boundaries in non-linear systems.
Cellular Automata
Discrete systems composed of a grid of cells that evolve according to simple local rules but generate complex global behaviors. Model the emergence of structures and self-organization phenomena in spatial systems.