Introduction: stability and pattern formation in networks of dynamical systems.
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Action Potentials↗
Biomedical subjects
Louis M Pecora
Publications and source records attributed to Louis M Pecora.
Analytical coupling detection in the presence of noise and nonlinearity.
A rigorous analytical approach is developed to test for the existence of a continuous nonlinear functional relationship between systems. We compare the application of this nonlinear local technique to the existing analytical linear global approach in the setting of increasing additive noise. For natural systems with unknown levels of noise and nonlinearity, we propose a general framework for detecting coupling. Lastly, we demonstrate the applicability of this method to detect coupling between simultaneous, experimentally measured, intracellular voltages between neurons within a mammalian neuronal network.
Animals↗
Synchronization in small-world systems.
We quantify the dynamical implications of the small-world phenomenon by considering the generic synchronization of oscillator networks of arbitrary topology. The linear stability of the synchronous state is linked to an algebraic condition of the Laplacian matrix of the network. Through numerics and analysis, we show how the addition of random shortcuts translates into improved network synchronizability. Applied to networks of low redundancy, the small-world route produces synchronizability more efficiently than standard deterministic graphs, purely random graphs, and ideal constructive schemes. However, the small-world property does not guarantee synchronizability: the synchronization threshold lies within the boundaries, but linked to the end of the small-world region.
Models, Theoretical↗
Reconstructing embedding spaces of coupled dynamical systems from multivariate data.
A method for reconstructing dimensions of subspaces for weakly coupled dynamical systems is offered. The tool is able to extrapolate the subspace dimensions from the zero coupling limit, where the division of dimensions as per the algorithm is exact. Implementation of the proposed technique to multivariate data demonstrates its effectiveness in disentangling subspace dimensionalities also in the case of emergent synchronized motions, for both numerical and experimental systems.
Journal Article↗