Dynamics of Two Coupled van der Pol Oscillators with Delay Coupling Revisited

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Richard Rand
Richard Rand
2
Mark Gluzman
Mark Gluzman
1 Cornell University

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The problem of two van der Pol oscillators coupled by velocity delay terms was studied by Wirkus and Rand in 2002 [5]. The small-𝜺𝜺 analysis resulted in a slow flow which contained delay terms. To simplify the analysis, Wirkus and Rand followed a common procedure of replacing the delay terms by non-delayed terms, a step said to be valid for small 𝜺𝜺, resulting in a slow flow which was an ODE rather than a DDE (delay-differential equation). In the present paper we consider the same problem but leave the delay terms in the slow flow, there by offering an evaluation of the approximate simplification made in [5].

Funding

No external funding was declared for this work.

Conflict of Interest

The authors declare no conflict of interest.

Ethical Approval

No ethics committee approval was required for this article type.

Data Availability

Not applicable for this article.

Richard Rand. 2017. \u201cDynamics of Two Coupled van der Pol Oscillators with Delay Coupling Revisited\u201d. Global Journal of Science Frontier Research - F: Mathematics & Decision GJSFR-F Volume 17 (GJSFR Volume 17 Issue F5): .

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Journal Specifications

Crossref Journal DOI 10.17406/GJSFR

Print ISSN 0975-5896

e-ISSN 2249-4626

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GJSFR-F Classification: MSC 2010: 00A69
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v1.2

Issue date

August 24, 2017

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English

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The problem of two van der Pol oscillators coupled by velocity delay terms was studied by Wirkus and Rand in 2002 [5]. The small-𝜺𝜺 analysis resulted in a slow flow which contained delay terms. To simplify the analysis, Wirkus and Rand followed a common procedure of replacing the delay terms by non-delayed terms, a step said to be valid for small 𝜺𝜺, resulting in a slow flow which was an ODE rather than a DDE (delay-differential equation). In the present paper we consider the same problem but leave the delay terms in the slow flow, there by offering an evaluation of the approximate simplification made in [5].

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Dynamics of Two Coupled van der Pol Oscillators with Delay Coupling Revisited

Mark Gluzman
Mark Gluzman
Richard Rand
Richard Rand Cornell University

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