It is a well known fact that the local stability of an equilibrium point in a system of ordinary differential equations doesnot necessarily imply its global stability. However, the usual methods used in the analysis of stability of equilibrium points in population models establishes only local stability. The restriction to sufficiently small perturbations of the initial conditions frequently ru...

This paper investigates Merton’s portfolio problem in a rough stochastic environment described by Volterra Heston model. The model has non-Markovian and non-semimartingale structure. By considering an auxiliary random process, we solve the optimization with martingale optimality principle. Optimal strategies for power exponential utilities are derived semi-closed form solutions depending on res...

Based on the classic Lotlk-Volterra cooperation model, we establish a time-delay model of which a species cannot survive independently. By continuation theorem, we discuss existence of positive periodic solutions of the model.

Two formulations of a nonlinear model predictive control scheme based on the second-order Volterra series model are presented. The lirst formulation determines the control action using successive substitution, and the second method directly solves a fourth-order nonlinear programming problem on-line. One case study is presented for the SISO control of an isothermal reactor which utilizes the fi...

We develop a theoretical context in which to study the future-sequential regularization method developed by J. V. Beck for the Inverse Heat Conduction Problem. In the process, we generalize Beck’s ideas and view that method as one in a large class of regularization methods in which the solution of an ill-posed first-kind Volterra equation is seen to be the limit of a sequence of solutions of we...

Volterra series expansions are widely used in analyzing and solving the problems of non-linear dynamical systems. However, the problem that the number of terms to be determined increases exponentially with the order of the expansion restricts its practical application. In practice, Volterra series expansions are truncated severely so that they may not give accurate representations of the origin...

In this paper we carefully study the analysis involved with Volterra series. We address system-theoretic issues ranging from bounds on the gain and incremental gain of Volterra series operators to the existence of Volterra series operator inverses, and mathematical topics such as the relation between Volterra series operators and Taylor series. The proofs are complete, and use only the basic fa...

More than 20 years ago it was shown that adaptive Volterra filters can be used for telephone echo cancellation, but the inherent need for a large number of coefficients has inhibited their practical use. Recently, first attempts have been made to combat nonlinearities in the acoustic echo path of hands-free telephones, which are caused by low-cost audio components. As these attempts are based o...