117,316 research outputs found
Application of the general methods of Lyapunov functionals construction for Volterra difference equations
No full textAbstract: Lyapunov functionals are used usually for stability investigation of systems with aftereffect. The general method of Lyapunov functionals construction which was proposed and developed by Kolmanovskii and Shaikhet is used here for stochastic second type Volterra difference equations. It is shown
that using this method, there is a possibility to construct for a given equation, a sequence of extending stability regions.
Keywords: Difference equations, Method of Lyapunov functionals construction, Asymptotic stability.
1. STATEMEN
Stability of Equilibrium Points of Fractional Difference Equations with Stochastic Perturbations
No full textIt is supposed that the fractional difference equation xn+1=(μ+∑j=0kajxn−j)/(λ+∑j=0kbjxn−j), n=0,1,…, has an equilibrium point x^ and is exposed to additive stochastic perturbations type of Ã(xn−x^)ξn+1 that are directly proportional to the deviation of the system state xn from the equilibrium point x^. It is shown that known results in the theory of stability of stochastic difference equations that were obtained via V. Kolmanovskii and L. Shaikhet general method of Lyapunov functionals construction can be successfully used for getting of sufficient conditions for stability in probability of equilibrium points of the considered stochastic fractional difference equation. Numerous graphical illustrations of stability regions and trajectories of solutions are plotted
About stability of nonlinear stochastic difference equations
No full textUsing the method of Lyapunov functionals construction, it is shown that investigation of stability in probability of nonlinear stochastic difference equation with order of nonlinearity more than one can be reduced to the investigation of asymptotic mean square stability of the linear part of this equation
About integrability of solutions of stochastic difference Volterra equations
No full text16th IMACS World Congress 2000 On Scientific Computation, Applied Mathematics a
Mean Square Summability of Solution of Stochastic Difference Second-Kind Volterra Equation with Small Nonlinearity
No full text Stochastic difference second-kind Volterra equation with continuous time and small nonlinearity is considered. Via the general method of Lyapunov functionals construction, sufficient conditions for uniform mean square summability of solution of the considered equation are obtained.</p
Stability of the Positive Point of Equilibrium of Nicholson's Blowflies Equation with Stochastic Perturbations: Numerical Analysis
No full textKnown Nicholson's blowflies equation
(which is one of the most important models in
ecology) with stochastic perturbations is considered. Stability of the positive (nontrivial)
point of equilibrium of this equation and also a capability of its discrete analogue to
preserve stability properties of the original differential equation are studied. For this purpose,
the considered equation is centered around the positive equilibrium and linearized.
Asymptotic mean square stability of the linear part of the considered equation is used to
verify stability in probability of nonlinear origin equation. From known previous results
connected with B. Kolmanovskii and L. Shaikhet, general method of Lyapunov functionals
construction, necessary and sufficient condition of stability in the mean square sense in
the continuous case and necessary and sufficient conditions for the discrete
case are deduced. Stability conditions for the discrete analogue allow to determinate an admissible step of discretization for numerical simulation of solution trajectories. The trajectories of stable and unstable solutions of considered equations are simulated numerically
in the deterministic and the stochastic cases for different values of the parameters and of the
initial data. Numerous graphical illustrations of stability regions and solution trajectories are plotted
Going Beyond Counting First Authors in Author Co-citation Analysis
No full textThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Square Dancing with the Stars to Enhance Dynamic Hirschman Linkages?
No full textIn this Presidential Address, the author takes the reader on a reconnaissance of his life and time as a regional scientist. He points out scenery he found scintillating along the way, hoping that some may pick up the banner and chew on a few of the ideas for a while. He suggests a revisit to Albert O. Hirschman’s notion of key sectors and more empirical analysis related to Marcus Berliant’s and Masahisa Fujita’s notion of knowledge creation and transfer.Presidential Address, San Antonio, Texas, March 29, 2014 (53rd Meetings of the Southern Regional Science Association
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