Class Of Volterra Research Articles

Assessment of the Potential Capacity of Carbon Sequestration of forest

Climate change poses a great threat to human survival, and therefore strong actions are needed to reduce the amount of greenhouse gases in the atmosphere in order to mitigate the effects of climate change, and forests play an important role in the process of greenhouse gas sequestration. To assess the carbon sequestration capacity of forests, this paper develops a carbon sequestration model to measure the amount of carbon sequestered in forests: first, an overview of the carbon sequestration content of forest vegetation is given, and various influencing factors affecting this content are listed. Then, the entropy weight method and the topsis integrated evaluation method were used to determine the effects of vegetation type, age and geography of the forest on the amount of carbon sequestered in the forest. After that, the changes of CO2 sequestration in the forest over time were further explored using Volterra class. In addition, the benefits and longevity of forest products are then integrated to determine how much CO2 can be sequestered by the forest and its products over time.

A Symbolic Method for Solving a Class of Convolution-Type Volterra–Fredholm–Hammerstein Integro-Differential Equations under Nonlocal Boundary Conditions

Integro-differential equations involving Volterra and Fredholm operators (VFIDEs) are used to model many phenomena in science and engineering. Nonlocal boundary conditions are more effective, and in some cases necessary, because they are more accurate measurements of the true state than classical (local) initial and boundary conditions. Closed-form solutions are always desirable, not only because they are more efficient, but also because they can be valuable benchmarks for validating approximate and numerical procedures. This paper presents a direct operator method for solving, in closed form, a class of Volterra–Fredholm–Hammerstein-type integro-differential equations under nonlocal boundary conditions when the inverse operator of the associated Volterra integro-differential operator exists and can be found explicitly. A technique for constructing inverse operators of convolution-type Volterra integro-differential operators (VIDEs) under multipoint and integral conditions is provided. The proposed methods are suitable for integration into any computer algebra system. Several linear and nonlinear examples are solved to demonstrate the effectiveness of the method.

Alternative criteria for boundedness of one class of integral operators in Lebesgue spaces

The paper discusses weighted Hardy type inequalities for a certain class of Volterra type integral operators with kernels. Criteria for the validity of the presented inequalities are found, which are different from the criteria obtained earlier.

A new numerical method for a class of Volterra and Fredholm integral equations

In the present work, we introduce a new numerical method based on a strong version of the mean-value theorem for integrals to solve quadratic Volterra integral equations and Fredholm integral equations of the second kind, for which there are theoretical monotonic non-negative solutions. By means of an equality theorem, the integral that appears in the aforementioned equations is transformed into one that enables a more accurate numerical solution with fewer calculations than other previously described methods. Convergence analysis is given.

Numerical solution of Volterra–Fredholm integral equations using the collocation method based on a special form of the Müntz–Legendre polynomials

This paper presents a computational technique based on a special family of the Müntz–Legendre polynomials to solve a class of Volterra–Fredholm integral equations. The relationship between the Jacobi polynomials and Müntz–Legendre polynomials, in a particular state, are expressed. The proposed method reduces the integral equation into algebraic equations via the Chebyshev–Gauss–Lobatto points, so that the system matrix coefficients are obtained by the least squares approximation method. The useful properties of the Jacobi polynomials are exploited to analyze the approximation error. The performance and accuracy of our method are examined with some illustrative examples.

Robust cycles in Kolmogorov–Lotka–Volterra class of models with intraspecific co-operation

Using the Andronov–Hopf bifurcation theorem and the Poincaré–Bendixson Theorem, we explore robust cyclical possibilities in Kolmogorov–Lotka–Volterra class of models with positive intraspecific cooperation (in the form of social networks) in the prey population. We find that this additional feedback effect of intraspecific cooperation introduces nonlinearities which modify the cyclical outcomes of the model. We show that the cyclical outcomes are more robust than in the existing literature in this area due to introduction of such non-linearities. We also demonstrate the possibilities of multiple limit cycles under certain situations.

Numerical solution of Volterra–Fredholm integral equations based on [formula omitted]-SVR method

In this paper, we try to study the numerical methods for solving integral equations from a new perspective—machine learning method. By means of the idea of kernel ε-support vector regression machine (ε-SVR), we construct an optimization modeling for a class of Volterra–Fredholm integral equations and propose a novel numerical method for solving them. The proposed method has a certain versatility and can be used to solve some other kinds of integral equations. In order to verify the effectiveness of the proposed method, we perform a series of comparative experiments with six specific Volterra–Fredholm integral equations and a method proposed in Wang et al. (2014). Experimental results show that the proposed method has a good approximation property.

3/2 -stability conditions for a class of Volterra–Levin equations

In this paper, a generalized Volterra–Levin equation is considered. 3/2-stability conditions are established for ensuring that the zero solution of the equation is uniformly stable, asymptotically stable and globally asymptotically stable. Further results are obtained under nonnegativity assumption. The main results are new and different from the known results.

Truncation order and its effect in a class of nonlinear systems

Fundamental results are established for truncation order and its effect in the Volterra class of nonlinear systems. These results provide a significant insight into the analytical relationships among truncation order, truncation error, and estimation error for the output spectra of nonlinear systems, and also lead to the development of novel methods for choosing the truncation order and excitation magnitudes for accurate determination of nonlinear frequency response components. These results should be important in the kernel estimation and frequency domain analysis of nonlinear systems on the basis of the Volterra series, structure and order selection of block-oriented nonlinear systems with polynomial nonlinearity. The results also provide a much improved version of the multi-level excitation method for system analysis and identification.

Asymptotic periodicity and almost automorphy for a class of Volterra integro‐differential equations

This work deals with the existence of asymptotically periodic (resp. asymptotically almost automorphic) solutions for a class of Volterra integro‐differential equations. As application, we examine sufficient conditions for the existence of asymptotically periodic (resp. asymptotically almost automorphic) mild solutions of an equation arising in the study of heat conduction in materials with memory. Copyright © 2012 John Wiley & Sons, Ltd.

Asymptotic Comparison of the Solutions of Linear Time-Delay Systems with Point and Distributed Lags with Those of Their Limiting Equations

This paper investigates the relations between the particular eigensolutions of a limiting functional differential equation of any order, which is the nominal (unperturbed) linear autonomous differential equations, and the associate ones of the corresponding perturbed functional differential equation. Both differential equations involve point and distributed delayed dynamics including Volterra class dynamics. The proofs are based on a Perron-type theorem for functional equations so that the comparison is governed by the real part of a dominant zero of the characteristic equation of the nominal differential equation. The obtained results are also applied to investigate the global stability of the perturbed equation based on that of its corresponding limiting equation.

Further results on some singular linear stochastic differential equations

A class of Volterra transforms, preserving the Wiener measure, with kernels of Goursat type is considered. Such kernels satisfy a self-reproduction property. We provide some results on the inverses of the associated Gramian matrices which lead to a new self-reproduction property. A connection to the classical reproduction property is given. Results are then applied to the study of a class of singular linear stochastic differential equations together with the corresponding decompositions of filtrations. The studied equations are viewed as non-canonical decompositions of some generalized bridges.

The three-dimensional generalized Lotka–Volterra systems

This work is devoted to the study of periodic solutions of generalized Lotka–Volterra systems in three dimensions. The group A3 of isometries of the regular tetrahedron acts on the twelve-dimensional space of such systems. We find four components (modulo the action of A3) of the center variety, i.e. the semi-algebraic subset consisting of systems with a family of periodic solutions (which degenerate at the center). We focus attention on the component which consists of systems X0 with an invariant plane L0 transversal to the coordinate axes and with a (partial) first integral on L0. Under the assumption of normal hyperbolicity of X0 along L0 we begin study of limit cycles appearing for a perturbed system (in the Lotka–Volterra class). The linearization of the problem leads to the problem of zeroes of certain Poincare–Melnikov integrals of a new type. We determine the asymptotic behavior of these integrals near two critical values of the partial first integral of the restricted system X0|L0. We also study the situation near the intersection of different components of the center variety.

Associated Linear Equations for Volterra operators

Non-linear time-invariant systems may be sometimes represented in the time-domain by a Volterra series which is a non-parametric, time-domain representation, or in the frequency-domain by the so-called higher-order frequency response functions (HFRFs). A non-parametric model in the time-domain gives very little insight into the intimate details of the non-linear system. Conversely the HFRFs are complicated in shape and are difficult to analyse. The graphical display of the HFRFs has the disadvantage of been multidimensional. It is known that the nth-order Volterra operator is a multi-linear-function of a combination of input signals. In fact, Hammerstein and Duffing type systems possess a linear relationship between the nth-order Volterra operator response and inputs composed of a combination of lower-order Volterra operators. This characteristic is used here to model the behaviour of the Volterra operators by linear equations that map the nth-order operator from an excitation of the same order produced by a combination of lower-order operators. This group of equations is referred to here as the Associated Linear Equations (ALEs). These ALEs can be used in simulation, control and as an analytical tool for the Volterra class of non-linear systems. The main advantage is that theory that up to today has been limited to linear systems can be used on this kind of non-linear systems allowing simpler manipulations.

On the solution of a class of Volterra integral equations of the first kind

On the solution of a class of Volterra integral equations of the first kind

A Short Note on Asymptotic Estimates of Stability Regions for a Certain Class of Volterra Integro‐Differential Equations

A Short Note on Asymptotic Estimates of Stability Regions for a Certain Class of Volterra Integro‐Differential Equations

On a class of Volterra and Fredholm non-linear integral equations

This paper concerns the existence and uniqueness of non-negative solutions of non-linear Volterra integral equations of the typeandwhere the kernel function k(.,.) is non-negative and sufficiently smooth, and either 0 < p < 1 or – 1 < p < 1. We will consider also the corresponding Fredholm equationsand