scholarly journals Algorithm for Rigorous Integration of Delay Differential Equations and the Computer-Assisted Proof of Periodic Orbits in the Mackey–Glass Equation

2017 ◽  
Vol 18 (6) ◽  
pp. 1299-1332 ◽  
Author(s):  
Robert Szczelina ◽  
Piotr Zgliczyński
Keyword(s):  
Differential Equations ◽  
Periodic Orbits ◽  
Delay Differential Equations ◽  
Computer Assisted ◽  
Computer Assisted Proof ◽  
Delay Differential

Control of Chaos in Networks with Delay: A Model for Synchronization of Cortical Tissue

1994 ◽  
Vol 6 (6) ◽  
pp. 1141-1154 ◽  
Author(s):  
C. Lourenço ◽  
A. Babloyantz
Keyword(s):  
Differential Equations ◽  
Periodic Orbits ◽  
Delay Differential Equations ◽  
Chaotic Dynamics ◽  
Cortical Activity ◽  
Inhibitory Neurons ◽  
Unstable Periodic Orbits ◽  
Cortical Tissue ◽  
Control Of Chaos ◽  
Delay Differential

The unstable periodic orbits of chaotic dynamics in systems described by delay differential equations are considered. An orbit is stabilized successfully, using a method proposed by Pyragas. The system under investigation is a network of excitatory and inhibitory neurons of moderate size, describing cortical activity. The relevance of the results for synchronized cortical activity is discussed.

Search for Periodic Orbits in Delay Differential Equations

2014 ◽  
Vol 24 (06) ◽  
pp. 1450084 ◽  
Author(s):  
Romina Cobiaga ◽  
Walter Reartes
Keyword(s):  
Dynamical Systems ◽  
Differential Equations ◽  
Periodic Orbits ◽  
Heuristic Search ◽  
Delay Differential Equations ◽  
Anharmonic Oscillator ◽  
Analysis Method ◽  
Van Der Pol ◽  
Homotopy Analysis ◽  
Delay Differential

In a previous paper, we developed a new way to apply the Homotopy Analysis Method (HAM) in the search for periodic orbits in dynamical systems modeled by ordinary differential equations. This method differs from the original in the heuristic search of the frequencies of the cycles. In this paper, we show that the method can be extended to the search for periodic orbits in delay differential equations. Herein, this methodology is applied twice, firstly in an equation of van der Pol type and secondly in an anharmonic oscillator, both systems with a delayed feedback.

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