Global hopf bifurcation
WebThe findings show that the age structure and delay can produce Hopf bifurcation for an SEIRS model. The numerical examples are executed to illustrate the theoretical results. Keywords: SEIRS Epidemic Model; Age-Structure ... Li M, Muldowney JS, Van den Driessche P , Global stability of SEIRS models in epidemiology, Can Appl Math Q … WebThe local and global stability of the positive equilibrium is presented. The existence of Hopf bifurcation around the positive equilibrium is observed. Further, by using the normal form theory and center manifold approach, we derive the explicit formulas determining the stability of bifurcating periodic solutions and the direction of Hopf ...
Global hopf bifurcation
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WebFurther, particular attention is focused on the existence of the global Hopf bifurcation. By using the global Hopf bifurcation theory due to Wu [1998], we show that the local Hopf bifurcation of (1) implies the global Hopf bifurcation after the second critical value of the delay τ. Finally, numerical simulation results are given to support the ... WebIn this article, we studied global stability and Hopf bifurcation of a newly delayed cooperative species model with density-dependent diffusion. When τ = 0 , we investigated the persistence properties in the case of self-diffusion and global stability of positive equilibrium by constructing Lyapunov function, see Fig. 2 , Fig. 3 , Fig. 4 , Fig ...
WebIn addition, the direction of Hopf bifurcation and stability of the periodic solutions bifurcating from the trivial equilibrium are determined based on the normal form theory and center manifold theorem. Moreover, employing the global Hopf bifurcation theory due to [Wu, 1998], we study the global existence of periodic solutions. WebMar 24, 2024 · Thirdly, bifurcation analysis at these equilibria is investigated, and it is found that the system undergoes a sequence of bifurcations, including Hopf, degenerate Hopf bifurcation, homoclinic bifurcation, the cusp type Bogdanov–Takens bifurcation of codimension 2, and the focus type Bogdanov–Takens bifurcation of codimension 3 …
WebDec 28, 2024 · While the first bifurcation is a primary Hopfbifurcation to the ROs, a secondary Hopf bifurcation leads to a two-frequency regime where a low …
WebIn addition, we propose the existence of Hopf bifurcation of Codimension 2 and the coexistence of stable limit cycle and unstable limit cycle. In particular, we show that the …
WebJan 25, 2024 · We develop a global Hopf bifurcation theory for differential equations with a state-dependent delay governed by an algebraic equation, using the \(S^1\)-equivariant degree.We apply the global Hopf bifurcation theory to a model of genetic regulatory dynamics with threshold type state-dependent delay vanishing at the stationary state, for … check stuffing meaningWeb5. Global Continuation of the Local Hopf Bifurcation. In this section, we will study the global continuation of periodic solutions bifurcating from the point for is fixed in the interval .Further, the method we used here is based on the global Hopf bifurcating theorem for general functional differential equations introduced by Wu [].For convenience, we denote … flatscreen television repair boiseWebThe mathematical structure of a simple climate model is investigated. The model is governed by a system of two nonlinear, autonomous differential equations for the evolution in time of global temperature T and meridional ice-sheet extent L. The system’s solutions are studied by a combination of qualitative reasoning with explicit calculations, both … flat screen television mount jobWebMay 17, 2024 · The theoretical analysis indicates that local and global bifurcation can occur from the positive steady state with respect to bifurcation parameters. These … flat screen television furnitureWebGlobal bifurcations, which often occur when larger invariant sets of the system 'collide' with each other, or with equilibria of the system. ... If the eigenvalue is equal to −1, it is a period-doubling (or flip) bifurcation, and … flat screen television vectorWebJan 16, 2016 · In this paper, the effect of the two different delays on the dynamics of a three-species ratio-dependent predator-prey food-chain model is considered. By regarding the delay as the bifurcation parameter, the local stability of the positive equilibrium and the existence of Hopf bifurcation are investigated. Explicit formulas … check stvp expiryWebWe study the homotopical and homological properties of the attractors evolving from a generalized Hopf bifurcation. We consider the Lorenz equations for parameter values … flat screen televisions