scholarly journals Delays and economic systems dynamics

2012 ◽  
Vol 53 ◽  
Author(s):  
Donatas Švitra
Keyword(s):  
Differential Equations ◽  
Mathematical Models ◽  
Delay Differential Equations ◽  
Bifurcation Theory ◽  
Economic Systems ◽  
Systems Dynamics ◽  
Delay Differential

Some mathematical models in economic systems with delay differential equations were presented. Analysis was made with the help of bifurcation theory.

Maximum response perturbation-based control of virus infection model with time-delays

2017 ◽  
Vol 32 (5) ◽  
Author(s):  
Gennady A. Bocharov ◽  
Yuri M. Nechepurenko ◽  
Michael Yu. Khristichenko ◽  
Dmitry S. Grebennikov
Keyword(s):  
Differential Equations ◽  
Mathematical Models ◽  
Delay Differential Equations ◽  
Chronic Phase ◽  
Lymphocytic Choriomeningitis ◽  
Steady States ◽  
Induced Response ◽  
Infection Model ◽  
Delay Differential ◽  
Optimal Disturbances

AbstractA new method for constructing the multi-modal impacts on the immune systemin the chronic phase of viral infection, based on mathematical models formulated with delay-differential equations is proposed. The so called, optimal disturbances, widely used in the aerodynamic stability theory for mathematical models without delays are constructed for perturbing the steady states of the dynamical system for maximizing the perturbation-induced response. The concept of optimal disturbances is generalized on the systems with delayed argument. An algorithm for computing the optimal disturbances is developed for such systems. The elaborated computational technology is tested on a system of four nonlinear delay-differential equations which represents the model of experimental infection in mice caused by lymphocytic choriomeningitis virus. The steady-state perturbations resulting in a maximum responsewere computed with the proposed algorithm for two types of steady states characterized by a low and a high levels of viral load. The possibility of correction of the infection dynamics and the restoration of virus-specific lymphocyte functioning of the immune system by perturbing the steady states is demonstrated.

A new Ф-generalized quasi metric space with some fixed point results and applications

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3157-3172
Author(s):  
Mujahid Abbas ◽  
Bahru Leyew ◽  
Safeer Khan
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Points ◽  
Periodic Solutions ◽  
Metric Space ◽  
Delay Differential Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Existence Of Periodic Solutions ◽  
Delay Differential

In this paper, the concept of a new ?-generalized quasi metric space is introduced. A number of well-known quasi metric spaces are retrieved from ?-generalized quasi metric space. Some general fixed point theorems in a ?-generalized quasi metric spaces are proved, which generalize, modify and unify some existing fixed point theorems in the literature. We also give applications of our results to obtain fixed points for contraction mappings in the domain of words and to prove the existence of periodic solutions of delay differential equations.

Mass Transport Modelling in Porous Media Using Delay Differential Equations

2006 ◽  
Vol 258-260 ◽  
pp. 586-591
Author(s):  
António Martins ◽  
Paulo Laranjeira ◽  
Madalena Dias ◽  
José Lopes
Keyword(s):  
Porous Media ◽  
Differential Equations ◽  
Mass Transport ◽  
Delay Differential Equations ◽  
Dispersion Model ◽  
Flow Characteristics ◽  
Convective Transport ◽  
Transport Modelling ◽  
Flow Field Characteristics ◽  
Delay Differential

In this work the application of delay differential equations to the modelling of mass transport in porous media, where the convective transport of mass, is presented and discussed. The differences and advantages when compared with the Dispersion Model are highlighted. Using simplified models of the local structure of a porous media, in particular a network model made up by combining two different types of network elements, channels and chambers, the mass transport under transient conditions is described and related to the local geometrical characteristics. The delay differential equations system that describe the flow, arise from the combination of the mass balance equations for both the network elements, and after taking into account their flow characteristics. The solution is obtained using a time marching method, and the results show that the model is capable of describing the qualitative behaviour observed experimentally, allowing the analysis of the influence of the local geometrical and flow field characteristics on the mass transport.

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