A CUBIC DIFFERENTIAL SYSTEM WITH NINE LIMIT CYCLES

Noel G. Lloyd; Jane M. Pearson

doi:10.11948/2012021

2012 Volume 2 Issue 3

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Noel G. Lloyd, Jane M. Pearson. A CUBIC DIFFERENTIAL SYSTEM WITH NINE LIMIT CYCLES[J]. Journal of Applied Analysis & Computation, 2012, 2(3): 293-304. doi: 10.11948/2012021

Citation:

Noel G. Lloyd, Jane M. Pearson. A CUBIC DIFFERENTIAL SYSTEM WITH NINE LIMIT CYCLES[J]. Journal of Applied Analysis & Computation, 2012, 2(3): 293-304. doi: 10.11948/2012021

A CUBIC DIFFERENTIAL SYSTEM WITH NINE LIMIT CYCLES

nstitue of Mathematics and Physics, Aberystwyth University, Penglais, Aberystwyth, Ceredigion UK SY23 3BZ

Abstract

Abstract

Advances in Computer Algebra software have made calculations possible that were previously intractable. Our particular interest is in the investigation of limit cycles of nonlinear differential equations. We describe some recent developments in handling very large computations involving resultants and present an example of a nonlinear differential system of degree three with nine small amplitude limit cycles surrounding a focus. We know of no examples of cubic systems with more than this number bifurcating from a fine focus, as opposed to a centre. Our example appears to be the first to have been obtained without recourse to some numerical calculation.
- Nonlinear differential equations /
- limit cycle /
- bifurcation /
- polynomial system
MSC: 34C07;68W30

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