Differential Equations with Applications to Biology

1991 Mathematics Subject 1999 American Mathematical A₁ applied assume assumption b₁ behavior Bogdanov-Takens bifurcation boundary bounded coefficients compact competition consider constant continuous continuous function convergence Corollary corresponding curve cycle Dalhousie University defined delay denote density differential equations diffusion disease dynamical systems eigenvalues endemic endemic equilibrium exists feedback Figure function given globally asymptotically stable Hence herd homoclinic Hopf bifurcation hormones implies infection initial Lemma lim sup linear loop Lyapunov function manifold Math Mathematics Subject Classification matrix monotone neutral nonlinear nonlocal nullcline obtain ordinary differential equations oscillations P₁ parameters periodic solutions population positive solution predator-prey problem Proof quasi-process reaction-diffusion equations satisfies Section sequence spatial species stable manifold stationary solutions stochastic Theorem 3.1 theory unique University values variable vector wave zero