Parameter identification for an abstract Cauchy problem by quasilinearization
Abstract : A parameter identification problem is considered in the context of a linear abstract Cauchy problem with a parameter-dependent evolution operator. Conditions are investigated under which the gradient of the state with respect to a parameter possesses smoothness properties which lead to local convergence of an estimation algorithm based on quasilinearization. Numerical results are presented concerning estimation of unknown parameters in delay-differential equations. (JHD)
Quasi-Newton methods for parameter estimation in functional differential equations
A state-space approach to parameter estimation in linear functional differential equations is developed using the theory of linear evolution equations. A locally convergent quasi-Newton type algorithm is applied to distributed systems with particular emphasis on parameters that induce unbounded perturbations of the state. The algorithm is computationally implemented on several functional differential equations, including coefficient and delay estimation in linear delay-differential equations.<<ETX>>
Global attractivity in time-delayed predator-prey systems
Abstract For a predator-prey model with time-delay due to gestation, criteria are obtained for persistence and global attractivity. The global attractivity criteria apply only to models with a decreasing prey isocline.