Multiple Nonlinear Oscillations in a𝔻3×𝔻3-Symmetrical Coupled System of Identical Cells with Delays | Zendy

Haijun Hu | Zendy; Li Liu | Zendy; Jie Mao | Zendy

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Multiple Nonlinear Oscillations in a𝔻3×𝔻3-Symmetrical Coupled System of Identical Cells with Delays

Author(s) -

Haijun Hu,

Li Liu,

Jie Mao

Publication year - 2013

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2013/417678

Subject(s) - nonlinear system , stability (learning theory) , scalar (mathematics) , bifurcation , differential equation , algorithm , mathematics , computer science , physics , mathematical analysis , geometry , quantum mechanics , machine learning

A coupled system of nine identical cells with delays and 3 × 3 -symmetry is considered. The individual cells are modelled by a scalar delay differential equation which includes linear decay and nonlinear delayed feedback. By analyzing the corresponding characteristic equations, the linear stability of the equilibrium is given. We also investigate the simultaneous occurrence of multiple periodic solutions and spatiotemporal patterns of the bifurcating periodic oscillations by using the equivariant bifurcation theory of delay differential equations combined with representation theory of Lie groups. Numerical simulations are carried out to illustrate our theoretical results.

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