• 대한수학회보
• /
• 제55권6호
• /
• pp.1921-1930
• /
• 2018

We consider a functional difference equation and use fixed point theory to obtain necessary and sufficient conditions for the asymptotic stability of its zero solution. At the end of the paper we apply our results to nonlinear Volterra infinite delay difference equations.

• 충청수학회지
• /
• 제20권3호
• /
• pp.287-296
• /
• 2007

Using the representation of the solution by means of the resolvent, we study the boundedness of the solutions of some Volterra difference equations.

• Kyungpook Mathematical Journal
• /
• 제60권1호
• /
• pp.163-175
• /
• 2020

The stability of a class of Volterra-type difference equations that include a generalized difference operator ∆_a is investigated using Krasnoselskii's fixed point theorem and some results are obtained. In addition, some examples are given to illustrate our theoretical results.

• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 2004년도 ICCAS
• /
• pp.1623-1628
• /
• 2004

In the 3-dimensional cyclic Lotka-Volterra equations, we show the solution on the invariant hyperplane. In addition, we show the existence of the invariant hyperplane by the center manifold theorem under the some conditions. With this result, we can lead the hyperplane of the n-dimensional cyclic Lotka-Volterra equaions. In other section, we study the 3- or 4-dimensional Hamiltonian Lotka-Volterra equations which satisfy the Jacobi identity. We analyze the solution of the Hamiltonian Lotka- Volterra equations with the functions called the split Liapunov functions by [4], [5] since they provide the Liapunov functions for each region separated by the invariant hyperplane. In the cyclic Lotka-Volterra equations, the role of the Liapunov functions is the same in the odd and even dimension. However, in the Hamiltonian Lotka-Volterra equations, we can show the difference of the role of the Liapunov function between the odd and the even dimension by the numerical calculation. In this paper, we regard the invariant hyperplane as the important item to analyze the motion of Lotka-Volterra equations and occur the chaotic orbit. Furtheremore, an example of the asymptoticaly stable and stable solution of the 3-dimensional cyclic Lotka-Volterra equations, 3- and 4-dimensional Hamiltonian equations are shown.

• 대한수학회논문집
• /
• 제37권3호
• /
• pp.939-955
• /
• 2022

In this paper, we study a first-order non-linear singularly perturbed Volterra integro-differential equation (SPVIDE). We discretize the problem by a uniform difference scheme on a Bakhvalov-Shishkin mesh. The scheme is constructed by the method of integral identities with exponential basis functions and integral terms are handled with interpolating quadrature rules with remainder terms. An effective quasi-linearization technique is employed for the algorithm. We establish the error estimates and demonstrate that the scheme on Bakhvalov-Shishkin mesh is O(N^-1) uniformly convergent, where N is the mesh parameter. The numerical results on a couple of examples are also provided to confirm the theoretical analysis.

• 전자공학회논문지D
• /
• 제35D권4호
• /
• pp.84-92
• /
• 1998

A program was developed to analyze the electrical characteristics and harmonic distrotion in a two-dimensional silicon BJT. The finite difference equations of the small signal and its second and thired harmonics for basic semiconductor equations are formulated treating the nonlinearity and time dependence with Volterra series and Taylor series. The soluations for three sets of simultaneous equations were obtained sequantially by a decoupled iteration method and each set was solved by a modified Stone's algorithm. Distortion magins and ac parameters such as input impedance and current gains are calculated with frequency and load resistance as parameters. The distortion margin vs. load resistancecurves show cancellation minima when the pahse of output voltage shifts. It is shown that the distortionof small signal characteristics can be reduced by reducing the base width, increasing the emitter stripe length and reducing the collector epitaxial layer doping concentration in the silicon BJT structure. The simulation program called TRADAP can be used for the design and optimization of transistors and circuits as well as for the calculation of small signal and distortion solutions.