On the Qualitative Analyses of Integro-Differential Equations with Constant Time Lag

2020 ◽  
Vol 14 (1) ◽  
pp. 57-63
Keyword(s):  
Differential Equations ◽  
Time Lag ◽  
Constant Time ◽  
Qualitative Analyses

scholarly journals Pointwise observation of the state given by complex time lag parabolic system

2017 ◽  
Vol 27 (1) ◽  
pp. 77-89
Author(s):  
Adam Kowalewski
Keyword(s):  
Boundary Condition ◽  
Parabolic System ◽  
Neumann Boundary Condition ◽  
Optimization Problems ◽  
Time Lag ◽  
Sufficient Conditions ◽  
Neumann Boundary ◽  
The State ◽  
Constant Time ◽  
Time Lags

AbstractVarious optimization problems for linear parabolic systems with multiple constant time lags are considered. In this paper, we consider an optimal distributed control problem for a linear complex parabolic system in which different multiple constant time lags appear both in the state equation and in the Neumann boundary condition. Sufficient conditions for the existence of a unique solution of the parabolic time lag equation with the Neumann boundary condition are proved. The time horizon T is fixed. Making use of the Lions scheme [13], necessary and sufficient conditions of optimality for the Neumann problem with the quadratic performance functional with pointwise observation of the state and constrained control are derived. The example of application is also provided.

Digital Model of Bench-Marking for Development of Competitive Advantage

2018 ◽  
pp. 288-303 ◽  
Author(s):  
Vardan Mkrttchian ◽  
Alexander Bershadsky ◽  
Alexey Finogeev ◽  
Artiom Berezin ◽  
Irina Potapova
Keyword(s):  
Differential Equations ◽  
Competitive Advantage ◽  
Time Lag ◽  
Digital Model ◽  
Nonlinear Feedback ◽  
Van Der Pol ◽  
Market Interaction ◽  
Digital Modeling ◽  
Working Out ◽  
Aggregate System

The chapter deals with the problems of digital modeling and the study of the interaction of the companies competing within the framework of the bench-marking process for definition, understanding and working out the strategy of effective functioning and increasing competitiveness. The companies are considered in the organizational field, representing iterative aggregate system of a big order with a nonlinear feedback where the order is defined by the number of differential equations. The system is described by coupled Van Der Pol differential equations with random right parts and a time lag. The model is built on the example of the market interaction of the two largest retailer networks. The developed model shows the mechanism of competition of the companies' pairs which are suggested to be investigated within the framework of the bench-marking concept.

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