## Differential Equations with Applications to Biology |

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### Contents

15 | |

Differential and Stochastic Epidemic Models | 31 |

General Recruitment Models for Sexually Transmitted Diseases | 45 |

Stability and Bifurcation of a Simple Neural Network with Multiple | 65 |

The Emergence of LargeScale Phenomena from | 81 |

On the Formation of Scroll Waves in an Anisotropic Ventricular | 97 |

Natural Selection as an Extensive Form Game | 119 |

Bifurcation Aspects for some Delayed Population Models with Diffusion | 143 |

Bifurcation Structure of Stationary Solutions of a LotkaVolterra | 293 |

Stability Domain of a Chemostat System with Delay | 307 |

Rich Dynamics of GauseType RatioDependent PredatorPrey System | 325 |

Differentiability with Respect to Delays for a Neutral Differential | 339 |

Renormalizations for Trimodal Maps | 353 |

A Generalization of Variation of Parameters and Lyapunovs Method | 377 |

Homoclinic Bifurcations in a Diffusively Coupled Excitable System | 397 |

On Boundary Value Problems for Quasilinear Elliptic Equations | 419 |

Extinction and Persistence in a SizeStructured Discrete Competitive | 159 |

Global Attractivity in a Nonlocal ReactionDiffusion Model | 175 |

Practical Persistence in Stochastic Population Models | 205 |

Continuity of Resetting Curves for FitzHughNagumo Equations | 225 |

Nonlinear Propagation in Reaction Transport Systems | 251 |

Skew Product Flows of QuasiProcesses and Stabilities | 269 |

Global Stability for a General Population Model with Time Delays | 447 |

Feedback Loops Analysis for Chaotic Dynamics with an Application to | 473 |

BogdanovTakens Bifurcations in PredatorPrey Systems with Constant | 493 |

Appendix List of Participants | 507 |

### Common terms and phrases

1999 American Mathematical analysis applied assume assumption behavior Biol Bogdanov-Takens bifurcation bounded characteristic equation chemostat coefficients compact competition consider continuous function convergence Corollary corresponding curve cycle Dalhousie University defined delay denote density depends diffusion disease dynamical systems eigenvalues endemic equilibrium Equation 1.1 example exists feedback Figure fixed point given globally asymptotically stable Hence herd homoclinic Hopf bifurcation hormones implies inequality infection integral invariant Lemma limsup linear loop Lyapunov function manifold Markov operators Math Mathematics Subject Classification matrix monotone nonlinear nonlocal nontrivial nullcline obtain ordinary differential equations oscillations periodic orbit periodic solutions persistence perturbation population positive solution predator-prey problem Proof properties quasi-process reaction-diffusion equations respect satisfies Section sequence space spatial species stable manifold stationary solutions stochastic Theorem 3.1 theory trajectories trivial solution unique University variable vector Volume 21 wave zero