It is well known that for the two species autonomous competitive Lotka-Volterra model with no fixed point in the open positive quadrant, one of the species is driven to extinction, whilst the other population stabilises at its own carrying capacity. In this paper we prove a generalisation of this result to nonautonomous systems of arbitrary finite dimension. That is, for the n species nonautono...

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...

In this work, we study the Neumann initial-boundary value problem for a two-species chemotaxis system with Lotka-Volterra competition and signal production. Under rather weak clean condition of sub-quadratic type damping merely integrable initial data, establish global existence generalized solutions in an N dimensional bounded smooth domain.

This article presents a numerical method for solving nonlinear two-dimensional fractional Volterra integral equation. We derive the Hat basis functions operational matrix of order integration and use it to solve integro-di?erential equations. The is described illustrated with examples. Also, we give error analysis.

In the present paper we consider a family of non-Volterra quadratic stochastic operators depending on parameter $\alpha$ and study their trajectory behaviors. We find all fixed points for operator finite-dimensional simplex. construct some Lyapunov functions. A complete description set limit is given, show that such have ergodic property.

In all of these cases, one-dimensional coefficient swaths of the kernel are used, taking advantage of the ability to perform fast one-dimensional convolutions. Using multidimensional filters, however, has advantages. Filtering in multiple dimensions more easily addresses asymmetric nonlinearities that sometimes occur in practice. To generalize the division of the Volterra kernel to use multidim...

3 Example: Differentiating the Lotka-Volterra ODE system 2 3.1 The Lotka-Volterra ODE system . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 3.2 The derivatives of the Lotka-Volterra ODE system . . . . . . . . . . . . . . . . . . 3 3.3 Integration of the original and augmented Lotka-Volterra ODE system with the Runge-Kutta method . . . . . . . . . . . . . . . . . . . . . . . . . . . ....

For the past two decades, the Volterra series reduced-order modeling approach has been successfully used for the purpose of flutter prediction, aeroelastic control design, and aeroelastic design optimization. The approach has been less successful, however, when applied to other important aeroelastic phenomena, such as aerodynamically induced limit-cycle oscillations. Similar to the Taylor serie...

Abstract: A one dimensional heat equation in a semi-infinite medium controlled through a heat source depending on the delayed heat flux at the extremum is studied. By reducing the problem to a delayed Volterra integral equation with a weakly singular kernel, we find conditions on the initial datum and on the source term of the equation to control the asymptotic behaviour of the mean temperatures.

We consider the (n 1)-dimensional Lotka-Volterra system (arising in biological modelling of species interactions), and associate with it a family of n-dimensional systems having the same phase portrait. We obtain some results on global behaviour and convergence towards the equilibrium in the case where the LV system is “nearly symmetric” or “nearly cooperative” (that is, there exists a member o...