In this paper we suggest a fast numerical approach to treat problems of the hereditary linear viscoelasticity, which results in the system of elliptic partial differential equations in space variables , who’s coefficients are Volterra integral operators of the second kind in time. We propose to approximate the relaxation kernels by the product of purely timeand space-dependent terms, which is a...

For permanent and partially permanent, uniformly bounded Lotka-Volterra systems, we apply the Split Lyapunov function technique developed for competitive Lotka-Volterra systems to find new conditions that an interior or boundary fixed point of a Lotka-Volterra system with general species-species interactions is globally asymptotically stable. Unlike previous applications of the Split Lyapunov t...

Hirota’s bilinear technique is applied to some integrable lattice systems related to the Bäcklund transformations of the 2DToda, Lotka-Volterra and relativistic LotkaVolterra lattice systems, which include the modified Lotka-Volterra lattice system, the modified relativistic Lotka-Volterra lattice system, and the generalized BlaszakMarciniak lattice systems. Determinant solutions are constructe...

Dynamical behaviors of the competitive Lotka-Volterra system even for 3 species are not fully understood. In this paper, we study this problem from the perspective of the Lyapunov function. We construct explicitly the Lyapunov function using three examples of the competitive Lotka-Volterra system for the whole state space: (1) the general 2-species case, (2) a 3-species model, and (3) the model...

A new modeling approach for the spectral analysis of pulsewidth modulated (PWM) converters with independent inputs is developed. The key of this approach is to extend the Volterra functional series to nonlinear systems with multiple independent inputs. After formulating the state-space equations describing the dynamical behavior of PWM converters, the Volterra transfer function characterizing t...

We introduce the Favard spaces for resolvent families, extending some well-known theorems for semigroups. Furthermore, we show the relationship between these Favard spaces and the Lp-admissibility of control operators for scalar Volterra linear systems in Banach spaces, extending some results in [22]. Assuming that the kernel a(t) is a creep function which satisfies a(0+) > 0, we prove an analo...