Combined Application of Global Optimization and Nonlinear Dynamics to Detect State Resetting in Human Epilepsy

Biocomputing ◽

10.1007/978-1-4613-0259-9_8 ◽

2002 ◽

pp. 139-157 ◽

Cited By ~ 7

Author(s):

J. C. Sackellares ◽

L. D. Iasemidis ◽

P. Pardalos ◽

D.-S. Shiau

Keyword(s):

Nonlinear Dynamics ◽

Global Optimization ◽

Combined Application ◽

Human Epilepsy

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A Deterministic Global Optimization Algorithm for Problems with Nonlinear Dynamics

Nonconvex Optimization and Its Applications - Frontiers in Global Optimization ◽

10.1007/978-1-4613-0251-3_1 ◽

2004 ◽

pp. 1-23 ◽

Cited By ~ 3

Author(s):

C. S. Adjiman ◽

I. Papamichail

Keyword(s):

Nonlinear Dynamics ◽

Global Optimization ◽

Optimization Algorithm ◽

Deterministic Global Optimization ◽

Global Optimization Algorithm

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Application of nonlinear dynamics methods for quantitative and qualitative evaluation of properties of 2D models of S-chaos

Journal Of Applied Informatics ◽

10.37791/2687-0649-2021-16-1-125-143 ◽

2021 ◽

Vol 16 (91) ◽

pp. 125-143

Author(s):

Aleksei A. Gavrishev ◽

Keyword(s):

Nonlinear Dynamics ◽

Lower Bound ◽

Time Domain ◽

Initial Conditions ◽

Qualitative Evaluation ◽

Recurrence Analysis ◽

Combined Application ◽

Student Version ◽

The Time Domain ◽

Property Characteristic

In this article, based on the mathematical, numerical and computer modeling carried out by the combined application of E&F Chaos, Past, Fractan, Visual Recurrence Analysis, Eviews Student Version Lite programs, some of the well-known 2D models of S-chaos are modeled, the data obtained are studied using nonlinear dynamics methods and the fact of their relation or non-relation to chaotic (quasi-chaotic) processes is established. As a result, it was found that the time diagrams obtained for the studied 2D models of S-chaos have a complex noise-like appearance and are continuous in the time domain. The resulting spectral diagrams have both a complex noise-like and regular appearance and are continuous in the spectral regions. The obtained values of BDS-statistics show that some of the time implementations can be attributed to chaotic (quasi-chaotic) processes. Also, the obtained values of BDS-statistics show that the studied 2D models of S-chaos have a property characteristic of classical chaotic (quasi-chaotic) processes: the slightest change in the initial conditions leads to the generation of a new set of signals. The obtained values of the lower bound of the KS-entropy show that the studied models also have the properties of chaotic (quasi-chaotic). Taking into account the conducted research and data from known works [1–5], it is possible to conclude that 2D models of S-chaos can relate to chaotic (quasi-chaotic) processes.

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