The problem of the optimal state estimation is solved for the system described by the continuous, linear, n-dimensional ordinary differential equation with multiplicative and additive Wiener noises. The obtained solution essentially relies on the recently developed optimal filtering theory for Itô-Volterra systems. Copyright c ©2005 IFAC.

Ecological communities can lose their permanence if a predator or a competitor is removed: the remaining species no longer coexist. This well-known phenomenon is analysed for some low dimensional examples of Lotka-Volterra type, with special attention paid to the occurrence of hetero-clinic cycles.

We study stochastic perturbed Volterra equations of convolution type in an infinite dimensional case. Our interest is directed towards the existence and regularity of stochastic convolutions connected to the equations considered under some kind of perturbations. We use an operator theoretical method for the representation of solutions.

Abstract: In this paper, we investigate piecewise approximate solution for linear two dimensional Volterra integral equation, based on the interval approximation of the true solution by truncated Chebyshev series. By discretization respect to spatial and time variables, the solution is approximated by using collocation method. Analysis of discretization error is discussed and efficiency of the ...

Bilinear approach is applied to derive integrable multi-component generalizations of the socalled 1+1 dimensional special Toda lattice, the Volterra lattice, a simple differential-difference equation found by Adler, Moser, Weiss, Veselov and Shabat and another integrable lattice reduced from the discrete BKP equation. Their soliton solutions expressed by pfaffians and the corresponding bilinear...

Abstract This paper aims to developed a high-order and accurate method for the solution of one-dimensional Lotka-Volterra-diffusion with Numman boundary conditions. A fourth-order compact finite difference scheme spatial part combined implicit-explicit Runge Kutta in temporal are proposed. Furthermore, points discretized by using terms fourth order accuracy. key idea proposed is take full advan...

We present a method to construct superintegrable $n$-component Lotka-Volterra systems with $3n-2$ parameters. apply the $n$ components for $1 < n 6$, and several $n$-dimensional families. The are in one-to-one correspondence trees on vertices.

We study multidimensional stochastic volatility models in which the process is a positive continuous function of Volterra that can be not self-similar. The main results obtained this paper are generalization due, one-dimensional case, to Cellupica and Pacchiarotti (J. Theor. Probab. 34(2):682–727). state some (pathwise finite-dimensional) large deviation principles for scaled log-price as conse...

In this article, we analyze multi-dimensional Bohr (B,c)-almost periodic type functions. The main structural characterizations for the introduced classes of functions are established. Several applications our abstract theoretical results to Volterra integro-differential equations in Banach spaces provided, as well.

We study the local integrability at origin of a nine-parameter family three-dimensional Lotka–Volterra differential systems with (3:− 1:2)-resonance. give necessary and sufficient conditions on parameters that guarantee existence two independent first integrals coordinates. Additionally, we classify those cases where is linearizable.