Electron. J. Diff. Eqns., Vol. 2007(2007), No. 119, pp. 1-23.

Centres and limit cycles for an extended Kukles system

Joe M. Hill, Noel G. Lloyd, Jane M. Pearson

Abstract:
We present conditions for the origin to be a centre for a class of cubic systems. Some of the centre conditions are determined by finding complicated invariant functions. We also investigate the coexistence of fine foci and the simultaneous bifurcation of limit cycles from them.

Submitted August 10, 2007. Published September 6, 2007.
Math Subject Classifications: 34C07, 37G15.
Key Words: Nonlinear differential equations; invariant curves; limit cycles.

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Joe M. Hill
Institute of Mathematical and Physical Sciences
Aberystwyth University, Ceredigion SY23 3BZ, Wales, UK
email: jyh@aber.ac.uk
Noel G. Lloyd
Institute of Mathematical and Physical Sciences
Aberystwyth University, Ceredigion SY23 3BZ, Wales, UK
email: ngl@aber.ac.uk
Jane M. Pearson
Institute of Mathematical and Physical Sciences
Aberystwyth University, Ceredigion SY23 3BZ, Wales, UK
email: jmp@aber.ac.uk

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