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- Quadratic stochastic operator (2)
- Allee effect (1)
- Bifurcation (1)
- Consensus (1)
- Control (1)
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- Cubic stochastic matrix (1)
- Ecliptic Plane (1)
- Elongated shape (1)
- Emphysema (1)
- Environment (1)
- Holling type III functional response (1)
- Hopf bifurcation (1)
- Leslie-Gower predator-prey model (1)
- Lotka-Volterra prey-predator model (1)
- Lung disease (1)
- Mathematical Model (1)
- Mean ergodicity (1)
- Particle deposition (1)
- Particle shape (1)
- Phase diagram (1)
- Pollutants (1)
- Porous media (1)
- Poynting-Robertson drag (1)
- Prey refuge (1)
- Pulsatile flow (1)
- Resonance (1)
- Sarymsakov cubic stochastic matrix (1)
- Simulation (1)
- Stability (1)
- Three-body problem (1)
Articles 1 - 7 of 7
Full-Text Articles in Dynamic Systems
Bifurcation Analysis For Prey-Predator Model With Holling Type Iii Functional Response Incorporating Prey Refuge, Lazaar Oussama, Mustapha Serhani
Bifurcation Analysis For Prey-Predator Model With Holling Type Iii Functional Response Incorporating Prey Refuge, Lazaar Oussama, Mustapha Serhani
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we carried out the bifurcation analysis for a Lotka-Volterra prey-predator model with Holling type III functional response incorporating prey refuge protecting a constant proportion of the preys. We study the local bifurcation considering the refuge constant as a parameter. From the center manifold equation, we establish a transcritical bifurcation for the boundary equilibrium. In addition, we prove the occurrence of Hopf bifurcation for the homogeneous equilibrium. Moreover, we give the radius and period of the unique limit cycle for our system
Ganikhodjaev's Conjecture On Mean Ergodicity Of Quadratic Stochastic Operators, Mansoor Saburov, Khikmat Saburov
Ganikhodjaev's Conjecture On Mean Ergodicity Of Quadratic Stochastic Operators, Mansoor Saburov, Khikmat Saburov
Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences
A linear stochastic (Markov) operator is a positive linear contraction which preserves the simplex. A quadratic stochastic (nonlinear Markov) operator is a positive symmetric bilinear operator which preserves the simplex. The ergodic theory studies the long term average behavior of systems evolving in time. The classical mean ergodic theorem asserts that the arithmetic average of the linear stochastic operator always converges to some linear stochastic operator. While studying the evolution of population system, S.Ulam conjectured the mean ergodicity of quadratic stochastic operators. However, M.Zakharevich showed that Ulam's conjecture is false in general. Later, N.Ganikhodjaev and D.Zanin have generalized Zakharevich's example …
Sarymsakov Cubic Stochastic Matrices, Mansoor Saburov, Khikmat Saburov
Sarymsakov Cubic Stochastic Matrices, Mansoor Saburov, Khikmat Saburov
Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences
The class of Sarymsakov square stochastic matrices is the largest subset of the set of stochastic, indecomposable, aperiodic (SIA) matrices that is closed under matrix multiplication and any infinitely long left-product of the elements from any of its compact subsets converges to a rank-one (stable) matrix. In this paper, we introduce a new class of the so-called Sarymsakov cubic stochastic matrices and study the consensus problem in the multi-agent system in which an opinion sharing dynamics is presented by quadratic stochastic operators associated with Sarymsakov cubic stochastic matrices.
Two Dimensional Mathematical Study Of Flow Dynamics Through Emphysemic Lung, Jyoti Kori, Pratibha _
Two Dimensional Mathematical Study Of Flow Dynamics Through Emphysemic Lung, Jyoti Kori, Pratibha _
Applications and Applied Mathematics: An International Journal (AAM)
There are various lung diseases, such as chronic obstructive pulmonary disease, asthma, fibrosis, emphysema etc., occurred due to deposition of different shape and size particles. Among them we focused on flow dynamics of viscous air through an emphysemic lung. We considered lung as a porous medium and porosity is a function of tidal volume. Two dimensional generalized equation of momentum is used to study the flow of air and equation of motion is used to study the flow of nanoparticles of elongated shape. Darcy term for flow in porous media and shape factor for nonspherical nanoparticles are used in mathematical …
Qualitative Analysis Of A Modified Leslie-Gower Predator-Prey Model With Weak Allee Effect Ii, Manoj K. Singh, B. S. Bhadauria
Qualitative Analysis Of A Modified Leslie-Gower Predator-Prey Model With Weak Allee Effect Ii, Manoj K. Singh, B. S. Bhadauria
Applications and Applied Mathematics: An International Journal (AAM)
The article aims to study a modified Leslie-Gower predator-prey model with Allee effect II, affecting the functional response with the assumption that the extent to which the environment provides protection to both predator and prey is the same. The model has been studied analytically as well as numerically, including stability and bifurcation analysis. Compared with the predator-prey model without Allee effect, it is found that the weak Allee effect II can bring rich and complicated dynamics, such as the model undergoes to a series of bifurcations (Homoclinic, Hopf, Saddle-node and Bogdanov-Takens). The existence of Hopf bifurcation has been shown for …
Environmental Balance Through Optimal Control On Pollutants, Nita H. Shah, Foram A. Thakkar, Moksha H. Satia
Environmental Balance Through Optimal Control On Pollutants, Nita H. Shah, Foram A. Thakkar, Moksha H. Satia
Applications and Applied Mathematics: An International Journal (AAM)
Pollution, which is a very common term has been divided as primary pollutants and secondary pollutants. Primary pollutants are those who results directly from some process whereas secondary pollutants are caused due to intermixing and reaction of primary pollutants. These pollutants result into acid rain. In this paper, a mathematical model has been developed to study the environmental impact due to acid rain. Pollutants such as primary and secondary pollutants are the causes of acid rain. Control in terms of gases emitted by factories, smog, burning of coal and fossil fuels have been applied on primary pollutants, secondary pollutants and …
Resonance In The Motion Of A Geocentric Satellite Due To Poynting-Robertson Drag And Equatorial Ellipticity Of The Earth, Charanpreet Kaur, Binay K. Sharma, Sushil Yadav
Resonance In The Motion Of A Geocentric Satellite Due To Poynting-Robertson Drag And Equatorial Ellipticity Of The Earth, Charanpreet Kaur, Binay K. Sharma, Sushil Yadav
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, the problem of resonance in a motion of a geocentric satellite is numerically investigated under the consolidated gravitational forces of the Sun, the Earth including Earth’s equatorial ellipticity parameter and Poynting-Robertson (P-R) drag. We are presuming that bodies lying on an ecliptic plane are the Sun and the Earth, and satellite on orbital plane. Resonance is monitored between satellite’s mean motion and average angular velocity of the Earth around the Sun, and also between satellite’s mean motion and equatorial ellipticity parameter of the Earth. We also perform a systematic and thorough analysis in an attempt to understand …