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Articles 1 - 6 of 6
Full-Text Articles in Dynamic Systems
Global Stability And Bifurcation Analysis Of A Predator-Prey Model Involving Allee Effect And Monod-Haldane Functional Response, Resmawan Resmawan, Agus Suryanto, Isnani Darti, Hasan S. Panigoro
Global Stability And Bifurcation Analysis Of A Predator-Prey Model Involving Allee Effect And Monod-Haldane Functional Response, Resmawan Resmawan, Agus Suryanto, Isnani Darti, Hasan S. Panigoro
Mathematical Modelling and Numerical Simulation with Applications
In this paper, the complexity of the dynamic behavior of the interaction between prey and predator is studied. The predator-prey relationship involves Allee effects and Monod-Haldane functional response. The constructed model has been shown to have validity in several respects, including the existence and uniqueness of the solution, as well as its non-negativity and boundedness. Three equilibrium points, namely trivial, axial, and coexistence points, are found, including their global dynamics using the Lyapunov function together with the LaSalle's invariance principle. The effect of the predation conversion rate causes changes in the dynamic behavior of predators and prey, which is characterized …
(Si10-057) Effect Of Time-Delay On An Sir Type Model For Infectious Diseases With Saturated Treatment, R. P. Gupta, Arun Kumar
(Si10-057) Effect Of Time-Delay On An Sir Type Model For Infectious Diseases With Saturated Treatment, R. P. Gupta, Arun Kumar
Applications and Applied Mathematics: An International Journal (AAM)
This study presents the complex dynamics of an SIR epidemic model incorporating a constant time-delay in incidence rate with saturated type of treatment rate. The system is studied to observe the effect of time lag in the asymptotic stability of endemic equilibrium states. We also establish global asymptotic stability of both disease-free and endemic equilibrium states by Lyapunov direct method with the help of suitable Lyapunov functionals. The existences of periodic solutions are ensured for the suitable choice of delay parameter. Finally, we perform numerical simulations supporting the analytical findings as well as to observe the effect of time-delay. The …
On An Ecological Model Of Mutualisim Between Two Species With A Mortal Predator, Srinivasarao Thota
On An Ecological Model Of Mutualisim Between Two Species With A Mortal Predator, Srinivasarao Thota
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we study an ecological model of a three-space food chain consists of two logically growing mutual species and third species acts as a predator to second mutual species with Holling type II functional response. This model is constituted by a system of nonlinear decoupled ordinary differential equations. By using perturbed method, we identify the nature of the system at each equilibrium point and also global stability is investigated for this model using Lypanov function at the possible equilibrium points.
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
On The Existence Of Bogdanov-Takens Bifurcations, Zachary Deskin
On The Existence Of Bogdanov-Takens Bifurcations, Zachary Deskin
Graduate Theses/Dissertations
In bifurcation theory, there is a theorem (called Sotomayor's Theorem) which proves the existence of one of three possible bifurcations of a given system, provided that certain conditions of the system are satisfied. It turns out that there is a "similar" theorem for proving the existence of what is referred to as a Bogdanov-Takens bifurcation. The author is only aware of one reference that has the proof of this theorem. However, most of the details were left out of the proof. The contribution of this thesis is to provide the details of the proof on the existence of Bogdanov-Takens bifurcations.
Controllability Of An Eco-Epidemiological System With Disease Transmission Delay: A Theoretical Study, Samadyuti Haldar, Kunal Chakraborty, T. K. Kar
Controllability Of An Eco-Epidemiological System With Disease Transmission Delay: A Theoretical Study, Samadyuti Haldar, Kunal Chakraborty, T. K. Kar
Applications and Applied Mathematics: An International Journal (AAM)
This paper deals with the qualitative analysis of a disease transmission delay induced prey preda-tor system in which disease spreads among the predator species only. The growth of the preda-tors’ susceptible and infected subpopulations is assumed as modified Leslie–Gower type. Suffi-cient conditions for the persistence, permanence, existence and stability of equilibrium points are obtained. Global asymptotic stability of the system is investigated around the coexisting equilib-rium using a geometric approach. The existence of Hopf bifurcation phenomenon is also exam-ined with respect to some important parameters of the system. The criterion for disease a trans-mission delay the induced Hopf bifurcation phenomenon …