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Lyapunov analysis of the spatially discrete-continuous system dynamics
- Source :
- Chaos, Solitons & Fractals. 104:228-237
- Publication Year :
- 2017
- Publisher :
- Elsevier BV, 2017.
-
Abstract
- The spatially discrete-continuous dynamical systems, that are composed of a spatially extended medium coupled with a set of lumped elements, are frequently met in different fields, ranging from electronics to multicellular structures in living systems. Due to the natural heterogeneity of such systems, the calculation of Lyapunov exponents for them appears to be a challenging task, since the conventional techniques in this case often become unreliable and inaccurate. The paper suggests an effective approach to calculate Lyapunov exponents for discrete-continuous dynamical systems, which we test in stability analysis of two representative models from different fields. Namely, we consider a mathematical model of a 1D transferred electron device coupled with a lumped resonant circuit, and a phenomenological neuronal model of spreading depolarization, which involves 2D diffusive medium. We demonstrate that the method proposed is able reliably recognize regular, chaotic and hyperchaotic dynamics in the systems under study.
- Subjects :
- Lyapunov function
Computer simulation
Dynamical systems theory
General Mathematics
Applied Mathematics
Chaotic
General Physics and Astronomy
Statistical and Nonlinear Physics
Lyapunov exponent
01 natural sciences
Stability (probability)
010305 fluids & plasmas
System dynamics
Living systems
symbols.namesake
Control theory
0103 physical sciences
symbols
Statistical physics
010306 general physics
Mathematics
Subjects
Details
- ISSN :
- 09600779
- Volume :
- 104
- Database :
- OpenAIRE
- Journal :
- Chaos, Solitons & Fractals
- Accession number :
- edsair.doi...........9bf1910209283b388e5aa1a0844c62fe