### Abstract

A model equation containing a memory integral is posed. The extent of the memory, the relaxation time lambda , controls the bifurcation behavior as the control parameter R is increased. Small (large) lambda gives steady (periodic) bifurcation. There is a double eigenvalue at lambda equals lambda //1, separating purely steady ( lambda less than lambda //1) from combined steady/T-periodic ( lambda less than lambda //1) states with T yields infinity as lambda yields lambda //1** plus . Analysis leads to the co-existence of stable steady/periodic states and as R is increased, the periodic states give way to the steady states. Numerical solutions show that this behavior persists away from lambda equals lambda //1.

Original language | English (US) |
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Pages (from-to) | 171-188 |

Number of pages | 18 |

Journal | SIAM Journal on Applied Mathematics |

Volume | 46 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 1986 |

### ASJC Scopus subject areas

- Applied Mathematics

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## Cite this

*SIAM Journal on Applied Mathematics*,

*46*(2), 171-188. https://doi.org/10.1137/0146013