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Ordinary Differential Equations and Applied Dynamics Commons™
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- Keyword
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- Stability (3)
- Bionomic equilibrium (1)
- Central manifold theory (1)
- Chemical balance dynamics (1)
- Cloud droplets (1)
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- Collocation points (1)
- Exponential approximation (1)
- Fractional q-derivative (1)
- Fractional q-integral (1)
- Gaseous pollutants (1)
- Hantavirus infection model (1)
- Harvesting effort (1)
- Hopf bifurcation (1)
- Limit cycle (1)
- Matrix method (1)
- Multiple transport delays (1)
- Next generation matrix method (1)
- Numerical solution (1)
- Optimal tax (1)
- Particulate matters (1)
- Peripheral and central control loops (1)
- Q- calculus (1)
- Q-fractional system (1)
- Raindrops (1)
- Respiratory control (1)
- SIR model; Beddington-DeAngelis type nonlinear incidence rate (1)
- Simulation (1)
- System of nonlinear differential equations (1)
Articles 1 - 6 of 6
Full-Text Articles in Ordinary Differential Equations and Applied Dynamics
Dynamics In A Respiratory Control Model With Two Delays, Saroj P. Pradhan, Ferenc Hartung, Janos Turi
Dynamics In A Respiratory Control Model With Two Delays, Saroj P. Pradhan, Ferenc Hartung, Janos Turi
Applications and Applied Mathematics: An International Journal (AAM)
In this paper we study ventilation patterns in a set of parameter dependent nonlinear delay equations with two transport delays modeling the human respiratory control system with peripheral and central control loops. We present a convergent numerical scheme suitable to perform simulations when all disturbances and system parameters are known, then we consider the numerical identifiability of various system parameters based on ventilation data. We are especially interested in the identification of the transport delays in the control loops because these parameters are not measurable directly, but they have a strong influence on system stability/instability.
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.
Dynamics Of An Sir Model With Nonlinear Incidence And Treatment Rate, Balram Dubey, Preeti Dubey, Uma S. Dubey
Dynamics Of An Sir Model With Nonlinear Incidence And Treatment Rate, Balram Dubey, Preeti Dubey, Uma S. Dubey
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, global dynamics of an SIR model are investigated in which the incidence rate is being considered as Beddington-DeAngelis type and the treatment rate as Holling type II (saturated). Analytical study of the model shows that the model has two equilibrium points (diseasefree equilibrium (DFE) and endemic equilibrium (EE)). The disease-free equilibrium (DFE) is locally asymptotically stable when reproduction number is less than one. Some conditions on the model parameters are obtained to show the existence as well as nonexistence of limit cycle. Some sufficient conditions for global stability of the endemic equilibrium using Lyapunov function are obtained. …
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 …
An Exponential Matrix Method For Numerical Solutions Of Hantavirus Infection Model, Şuayip Yüzbaşi, Mehmet Sezer
An Exponential Matrix Method For Numerical Solutions Of Hantavirus Infection Model, Şuayip Yüzbaşi, Mehmet Sezer
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, a new matrix method based on exponential polynomials and collocation points is proposed to obtain approximate solutions of Hantavirus infection model corresponding to a class of systems of nonlinear ordinary differential equations. The method converts the model problem into a system of nonlinear algebraic equations by means of the matrix operations and the collocation points. The reliability and efficiency of the proposed scheme is demonstrated by the numerical applications and all numerical computations have been made by using a computer program written in Maple.