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Articles 1 - 7 of 7
Full-Text Articles in Control Theory
(R2167) Global Stability Of Seirs Model With Single Dose Vaccination In Varying Population, Govind Jha, Prabhat Mandal, Sarita Jha
(R2167) Global Stability Of Seirs Model With Single Dose Vaccination In Varying Population, Govind Jha, Prabhat Mandal, Sarita Jha
Applications and Applied Mathematics: An International Journal (AAM)
Understanding the evolution of infectious diseases within a dynamic population is essential for formulating effective public health strategies. This work introduces an enhanced SEIRS epidemic model that incorporates demographic variation and a single-dose vaccination strategy, supporting that immunity can be reduced over time. The model reflects diseases in which individuals may return to the susceptible state after recovery. Extending prior reduced three-dimensional models, this study develops a complete four-dimensional SEIRS framework, thereby increasing the model’s applicability to real-world scenarios. The inclusion of the full system presents greater analytical challenges. To overcome this, we extend the second additive compound matrix and …
Stability Of Cauchy's Equation On Δ+., Holden Wells
Stability Of Cauchy's Equation On Δ+., Holden Wells
Electronic Theses and Dissertations
The most famous functional equation f(x+y)=f(x)+f(y) known as Cauchy's equation due to its appearance in the seminal analysis text Cours d'Analyse (Cauchy 1821), was used to understand fundamental aspects of the real numbers and the importance of regularity assumptions in mathematical analysis. Since then, the equation has been abstracted and examined in many contexts. One such examination, introduced by Stanislaw Ulam and furthered by Donald Hyers, was that of stability. Hyers demonstrated that Cauchy's equation exhibited stability over Banach Spaces in the following sense: functions that approximately satisfy Cauchy's equation are approximated with the same level of error by functions …
Strong Stability Of A Class Of Difference Equations Of Continuous Time And Structured Singular Value Problem, Qian Ma, Keqin Gu, Narges Choubedar
Strong Stability Of A Class Of Difference Equations Of Continuous Time And Structured Singular Value Problem, Qian Ma, Keqin Gu, Narges Choubedar
SIUE Faculty Research, Scholarship, and Creative Activity
This article studies the strong stability of scalar difference equations of continuous time in which the delays are sums of a number of independent parameters tau_i, i = 1, 2, . . . ,K. The characteristic quasipolynomial of such an equation is a multilinear function of exp(-tau_i s). It is known that the characteristic quasipolynomial of any difference equation set in the form of one-delayper- scalar-channel (ODPSC) model is also in such a multilinear form. However, it is shown in this article that some multilinear forms of quasipolynomials are not characteristic quasipolynomials of any ODPSC difference equation set. The equivalence …
Strong Stability Of A Class Of Difference Equations Of Continuous Time And Structured Singular Value Problem, Qian Ma, Keqin Gu, Narges Choubedar
Strong Stability Of A Class Of Difference Equations Of Continuous Time And Structured Singular Value Problem, Qian Ma, Keqin Gu, Narges Choubedar
SIUE Faculty Research, Scholarship, and Creative Activity
This article studies the strong stability of scalar difference equations of continuous time in which the delays are sums of a number of independent parameters τi, i = 1, 2, . . . , K. The characteristic quasipolynomial of such an equation is a multilinear function of e−τis. It is known that the characteristic quasipolynomial of any difference equation set in the form of one-delay-per-scalar-channel (ODPSC) model is also in such a multilinear form. However, it is shown in this article that some multilinear forms of quasipolynomials are not characteristic quasipolynomials of any ODPSC difference equation set. The equivalence between …
On Local Asymptotic Stability Of Q-Fractional Nonlinear Dynamical Systems, Ilknur Koca, Elif Demirci
On Local Asymptotic Stability Of Q-Fractional Nonlinear Dynamical Systems, Ilknur Koca, Elif Demirci
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, locally asymptotic stability of q-fractional order nonlinear dynamical systems is introduced and studied. The sufficient conditions for local stability of such dynamical systems are obtained. Also, useful definitions of fractional order q-integrals and q-derivatives are recalled. Finally, a q-fractional order nonlinear dynamical model is considered.
Modelling The Dynamics Of A Renewable Resource Under Harvesting With Taxation As A Control Variable, B. Dubey, Atasi Patra, S. K. Sahani
Modelling The Dynamics Of A Renewable Resource Under Harvesting With Taxation As A Control Variable, B. Dubey, Atasi Patra, S. K. Sahani
Applications and Applied Mathematics: An International Journal (AAM)
The present paper describes a model of resource biomass and population with a non-linear catch rate function on resource biomass. The harvesting effort is assumed to be a dynamical variable. Tax on per unit harvested resource biomass is used as a tool to control exploitation of the resource. Pontryagin’s Maximum Principle is used to find the optimal control to maintain the resource biomass and population at an optimal level. A numerical simulation is also carried out to support the analytical results.
Modelling The Role Of Cloud Density On The Removal Of Gaseous Pollutants And Particulate Matters From The Atmosphere, Shyam Sundar, Rajan K. Sharma, Ram Naresh
Modelling The Role Of Cloud Density On The Removal Of Gaseous Pollutants And Particulate Matters From The Atmosphere, Shyam Sundar, Rajan K. Sharma, Ram Naresh
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, a six dimensional nonlinear mathematical model is proposed to study the effect of the density of cloud droplets (formed due to the presence of vapors in the atmosphere) on the removal of pollutants, both gaseous and particulate, from the atmosphere. We assume that there exist six nonlinearly interacting phases in the atmosphere i.e. the vapor phase, the phase of cloud droplets, the phase of raindrops, the phase of gaseous pollutants, the phase of particulate matters and the phase of gaseous pollutants absorbed in raindrops. It is further assumed that the dynamics of the system undergo ecological type …