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Generation of Local CA1 γ Oscillations by Tetanic Stimulation

Generation of Local CA1 γ Oscillations by Tetanic Stimulation

Published on: August 14, 2015

Turing instability in oscillator chains with nonlocal coupling.

R L Viana¹, F A dos S Silva, S R Lopes

¹Departamento de Física, Universidade Federal do Paraná, Caixa Postal 19044, 81531-990, Curitiba, Paraná, Brazil. viana@fisica.ufpr.br

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|May 24, 2011

Summary

This summary is machine-generated.

This study explores Turing instability in nonlinear oscillators. We found that nonlocal coupling, varying with distance, influences pattern formation in these systems.

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Area of Science:

Nonlinear dynamics
Pattern formation
Statistical physics

Background:

Turing instability drives pattern formation in reaction-diffusion systems.
Nonlocal coupling is crucial in many physical and biological systems.
Understanding coupling effects is key to predicting system behavior.

Purpose of the Study:

Investigate Turing instability conditions in 1D nonlinear oscillator chains.
Analyze the impact of nonlocal coupling, decreasing as a power law with distance.
Examine the transition from local to global coupling using a range parameter.

Main Methods:

Analytical investigation of system dynamics.
Numerical simulations to explore parameter space.
Power-law coupling model for spatial interactions.
Analysis of a nonlinear autocatalytic reaction-diffusion model.

Main Results:

Identified conditions for Turing instability under nonlocal coupling.
Demonstrated how the power-law decay of coupling strength influences pattern formation.
Showcased the role of the range parameter in bridging local and global coupling regimes.

Conclusions:

Nonlocal coupling significantly alters Turing instability thresholds and patterns.
The spatial decay of coupling is a critical factor in pattern emergence.
This work provides insights into pattern formation in extended nonlinear systems.