11 results
Search Results
2. Stability and bifurcation analysis of a stage structured predator prey model with time delay
- Author
-
Kar, T.K. and Jana, Soovoojeet
- Subjects
- *
STABILITY theory , *PREDATION , *MATHEMATICAL models , *TIME delay systems , *HOPF bifurcations , *COMPUTER simulation - Abstract
Abstract: In this paper we proposed and analyzed a prey predator system with stage-structured for the predator population. A time delay is incorporated due to the gestation for the matured predator. All the possible non-negative equilibria are obtained and their local as well as global behavior are studied. Choosing delay as a bifurcation parameter, the existence of the Hopf bifurcation of the system has been investigated. Moreover, we use the normal form method and the center manifold theorem to examine the direction of the Hopf bifurcation and the nature of the bifurcating periodic solution. Some numerical simulations are given to support the analytical results. Some interesting conclusions are obtained from our analysis and it is given at the end of the paper. [Copyright &y& Elsevier]
- Published
- 2012
- Full Text
- View/download PDF
3. Global stability and Hopf bifurcations of an SEIR epidemiological model with logistic growth and time delay.
- Author
-
Xu, Rui, Wang, Zhili, and Zhang, Fengqin
- Subjects
- *
STABILITY theory , *HOPF bifurcations , *COMPUTER simulation , *EPIDEMIOLOGICAL models , *LOGISTICS , *TIME delay systems - Abstract
In this paper, an SEIR epidemiological model with saturation incidence and a time delay describing the latent period of the disease is investigated, where it is assumed that the susceptible population is subject to logistic growth in the absence of the disease. By analyzing the corresponding characteristic equations, the local stability of a disease-free equilibrium and an endemic equilibrium is discussed. The existence of Hopf bifurcations at the endemic equilibrium is established. By means of Lyapunov functionals and LaSalle’s invariance principle, it is proved that if the basic reproduction number is less than unity, the disease-free equilibrium is globally asymptotically stable and the disease dies out; if the basic reproduction number is greater than unity, sufficient conditions are obtained for the global stability of the endemic equilibrium. Numerical simulations are carried out to illustrate some theoretical results. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
4. Stability and Hopf bifurcation analysis of a ratio-dependent predator–prey model with two time delays and Holling type III functional response.
- Author
-
Wang, Xuedi, Peng, Miao, and Liu, Xiuyu
- Subjects
- *
STABILITY theory , *HOPF bifurcations , *PREDATION , *INTERNATIONAL relations , *COMPUTER simulation - Abstract
In this paper, a delayed ratio-dependent predator–prey model with Holling type III functional response and stage structure for the predator is considered. By analyzing the corresponding characteristic equations, the local stability of each of the feasible equilibria of the system is addressed and the existence of Hopf bifurcations at the coexistence equilibrium is established. By utilizing normal form method and center manifold theorem, the explicit formulas which determine the direction of Hopf bifurcation and the stability of bifurcating period solutions are derived. Finally, numerical simulations supporting the theoretical analysis are given. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
5. Effects of additional food on an ecoepidemic model with time delay on infection.
- Author
-
Sahoo, Banshidhar and Poria, Swarup
- Subjects
- *
EPIDEMIOLOGICAL models , *TIME delay systems , *HOPF bifurcations , *STABILITY theory , *COMPUTER simulation - Abstract
We propose a predator–prey ecoepidemic model with parasitic infection in the prey. We assume infection time delay as the time of transmission of disease from susceptible to infectious prey. We examine the effects of supplying additional food to predator in the proposed model. The essential theoretical properties of the model such as local and global stability and in addition bifurcation analysis is done. The parameter thresholds at which the system admits a Hopf bifurcation are investigated in presence of additional food with non-zero time lag. The conditions for permanence of the system are also determined in this paper. Theoretical analysis results are verified through numerical simulations. By supplying additional food we can control predator population in the model. Most important observation is that we can control parasitic infection of prey species by supplying additional food to predator. Eliminating the most infectious individuals from the prey population, predator quarantine the infected prey and prevent the spreading of disease. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
- View/download PDF
6. Stability and Hopf bifurcation in a model of gene expression with distributed time delays.
- Author
-
Yongli Song, Yanyan Han, and Tonghua Zhang
- Subjects
- *
STABILITY theory , *HOPF bifurcations , *GENE expression , *TIME delay systems , *KERNEL (Mathematics) , *COMPUTER simulation , *MATHEMATICAL models - Abstract
In this paper, we consider the effect of distributed time delays on dynamics of a mathematical model of gene expression. Both the weak and strong delay kernels are discussed. Sufficient conditions for the local stability of the unique equilibrium are obtained. Taking the average delay as a bifurcation parameter, we investigate the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions by using the method of multiple time scales. Finally, numerical simulation is carried out to illustrate our theoretical results. It shows both subcritical and supercritical Hopf bifurcations can happen. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
- View/download PDF
7. Dynamical behavior of a food chain model with prey toxicity.
- Author
-
Li, Ya and Xue, Yumei
- Subjects
- *
EFFECT of poisons on plants , *HERBIVORES , *PLANT species , *FOOD chains , *HOPF bifurcations , *PREDATION , *COMPUTER simulation , *MATHEMATICAL models - Abstract
This paper deals with a three-dimensional plant-herbivore-predator model that incorporates explicitly the plant toxicity in plant-herbivore interactions. The existence and stability conditions of all the feasible equilibria are established. Our results indicate that plant toxicity may play a key role in the dynamical behavior of the system. By adding another plant species with a different toxicity level to this system, we derive threshold conditions on the invasion of the second plant species. The analysis indicates that several parameters may be critical to determine successful invasion. Numerical simulations are also provided to reinforce the theoretical conclusions. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
- View/download PDF
8. Hopf bifurcation analysis for a ratio-dependent predator–prey system with two delays and stage structure for the predator.
- Author
-
Deng, Lianwang, Wang, Xuedi, and Peng, Miao
- Subjects
- *
HOPF bifurcations , *PREDATION , *COMPUTER simulation , *MATHEMATICAL analysis , *NUMERICAL solutions to differential equations - Abstract
Abstract: The ratio-dependent theory is favored by researchers since it is more suitable for describing the relationship between predator and its prey. In this paper, a ratio-dependent predator–prey system with Holling type II functional response, two time delays and stage structure for the predator is investigated. Firstly, by choosing the two time delays as the bifurcation parameter, the sufficient conditions for the local stability and the existence of Hopf bifurcation with respect to both delays are established. Furthermore, based on the normal form method and center manifold theorem, explicit formulas are derived to determine the direction of Hopf bifurcation and stability of the bifurcating periodic solution. Finally, numerical simulations are given to verify the theoretical analysis. [Copyright &y& Elsevier]
- Published
- 2014
- Full Text
- View/download PDF
9. Hopf bifurcation analysis and amplitude control of the modified Lorenz system.
- Author
-
Wang, Xuedi, Deng, Lianwang, and Zhang, Wenli
- Subjects
- *
HOPF bifurcations , *CONTROL theory (Engineering) , *LORENZ equations , *CENTER manifolds (Mathematics) , *MATHEMATICS theorems , *COMPUTER simulation , *FEEDBACK control systems - Abstract
Abstract: This paper is concerned with the Hopf bifurcation analysis and amplitude control of the modified Lorenz system. The Hopf bifurcation of system is investigated by utilizing the Hopf bifurcation theory and the center manifold theorem firstly. Then the direction and stability of limit cycle emerging from Hopf bifurcation are determined by the designed controller. Moreover, the amplitude of limit cycle emerging from Hopf bifurcation is controlled by a nonlinear feedback controller. Finally, numerical simulations are given to verify theoretical analysis. [Copyright &y& Elsevier]
- Published
- 2013
- Full Text
- View/download PDF
10. Hopf bifurcation analysis of a system of coupled delayed-differential equations
- Author
-
Çelik, C. and Merdan, H.
- Subjects
- *
HOPF bifurcations , *COUPLED mode theory (Wave-motion) , *NUMERICAL solutions to delay differential equations , *CENTER manifolds (Mathematics) , *COMPUTER simulation , *PERIODIC functions - Abstract
Abstract: In this paper, we have considered a system of delay differential equations. The system without delayed arises in the Lengyel–Epstein model. Its dynamics are studied in terms of local analysis and Hopf bifurcation analysis. Linear stability is investigated and existence of Hopf bifurcation is demonstrated via analyzing the associated characteristic equation. For the Hopf bifurcation analysis, the delay parameter is chosen as a bifurcation parameter. The stability of the bifurcating periodic solutions is determined by using the center manifold theorem and the normal form theory introduced by Hassard et al. (1981) [7]. Furthermore, the direction of the bifurcation, the stability and the period of periodic solutions are given. Finally, the theoretical results are supported by some numerical simulations. [Copyright &y& Elsevier]
- Published
- 2013
- Full Text
- View/download PDF
11. Memory-based movement with spatiotemporal distributed delays in diffusion and reaction.
- Author
-
Song, Yongli, Wu, Shuhao, and Wang, Hao
- Subjects
- *
HOPF bifurcations , *SPATIAL memory , *ANIMAL mechanics , *ANIMAL species , *COMPUTER simulation , *DIFFUSION coefficients - Abstract
• Propose a general single species animal movement model with distributed delays in diffusion and reaction. • Investigate the impact of spatiotemporal delays on stability of memory-based model. • Obtain conditions for the occurrence of Hopf and steady state bifurcations. • Explore dynamics due to the interaction of Hopf and steady state bifurcations. In this paper, we investigate the spatiotemporal dynamics of a single-species model with spatiotemporal delays characterizing spatial memory and maturation. Through stability and bifurcation analysis, we find that the spatial memory-based diffusion coefficient, the spatiotemporal diffusive delay and spatiotemporal reaction delay have important effects on the dynamics of the model and their combined impact can cause the destabilization of the positive constant steady state and give rise to steady state and Hopf bifurcations. Taking the coefficient of spatial memory diffusion as the bifurcation parameter, the critical values of steady state and Hopf bifurcations are rigorously determined. Furthermore, we apply the theoretical results to a modified diffusive logistic model with predation and obtain spatially inhomogeneous steady states and spatially homogeneous and inhomogeneous periodic solutions via numerical simulations. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
Discovery Service for Jio Institute Digital Library
For full access to our library's resources, please sign in.