Investigation of Turing instability for the Gierer–Meinhardt model

The dependence of the emergence of Turing instability for a distributed system of nonlinear differential equations that describe hydra morphogenesis based on the oscillatory properties of the corresponding trajectories of the system was investigated. The limits in the parameter space that provide di...

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Published inBiophysics (Oxford) Vol. 62; no. 2; pp. 301 - 308
Main Authors Egorova, G. F., Pavlova, G. A., Afanasieva, O. S.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.03.2017
Springer Nature B.V
Subjects
Biological and Medical Physics
Biophysics
Comparative analysis
Complex Systems Biophysics
Differential equations
Emergence
Mathematical models
Morphogenesis
Nonlinear differential equations
Nonlinearity
Oscillations
Physics
Physics and Astronomy
Spatial analysis
Spatial distribution
Trajectory analysis
limit cycle
nonlinear differential equations with partial derivatives
self oscillations
diffusion Turing instability
dissipation structures
phase portrait
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Summary:The dependence of the emergence of Turing instability for a distributed system of nonlinear differential equations that describe hydra morphogenesis based on the oscillatory properties of the corresponding trajectories of the system was investigated. The limits in the parameter space that provide diffusive instability were obtained. The frequency and amplitude dependences of the resulting spatial self oscillations on the values of the main parameters were investigated. Comparative analysis of the properties of the distributed system and corresponding trajectories of the system was carried out and the analytical conclusions were confirmed by the solutions of the system that were found using MATLAB.
ISSN:0006-3509
1555-6654
DOI:10.1134/S0006350917020063