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...

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...

This article begins with a full description of the quadratic planar vector fields which display two centers. We follow method proposed by Chengzhi Li and provide more detailed analysis different types double centers using classification: Hamiltonian, reversible, Lotka-Volterra, Q4, currently used for fields. also describe completely possible phase portraits their Poincaré compactification. show...

The paper gives necessary and sufficient conditions providing regularity of solutions to stochastic Volterra equations with infinite delay on a ddimensional torus. The harmonic analysis techniques and stochastic integration in function spaces are used.

In this paper a closed form solution of a fractional integro-differential equation of Volterra type involving Mittag-Leffler function has been obtained using straight forward technique of Sumudu transform. Some particular cases have also been considered.

This work considers behavioral modeling, parameter-reduction, and digital predistortion of radio frequency power amplifiers. Due to the use of modern digital modulation methods, contemporary power amplifiers are frequently subjected to signals characterized by considerable bandwidths and fast changing envelopes. As a result, traditional quasi-memoryless amplitude-to-amplitude (AM/AM) and amplit...

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...

Kernel-based modeling of dynamic systems has garnered a significant amount of attention in the system identification literature since its introduction to the field in [7]. While the method was originally applied to linear impulse response estimation in the time domain, the concepts have since been extended to the frequency domain for estimation of frequency response functions (FRFs) [6], as wel...

We survey continuous and discrete regularization methods for first-kind Volterra problems with continuous kernels. Classical regularization methods tend to destroy the non-anticipatory (or causal) nature of the original Volterra problem because such methods typically rely on computation of the Volterra adjoint operator, an anticipatory operator. In this survey we pay special attention to partic...