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Stability Analysis of a Nonautonomous Diffusive Predator-Prey Model with Disease in the Prey and Beddington-DeAngelis Functional Response. [PDF]
Biology (Basel)Zhang Y, Jiang T, Wang C, Shang Q.
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Bogdanov–Takens and Hopf Bifurcations Analysis of a Genetic Regulatory Network
Qualitative Theory of Dynamical Systems, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ming Liu, Fanwei Meng, Dongpo Hu
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Practical computation of normal forms of the Bogdanov–Takens bifurcation
Nonlinear Dynamics, 2011zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Peng, Guojun, Jiang, Yaolin
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Bogdanov–Takens bifurcation in a predator–prey model with age structure
Zeitschrift für angewandte Mathematik und Physik, 2020This paper deals with the Bogdanov-Takens bifurcation of a predator-prey model where the predator has an age structure. More precicely the following system is studied: \[\begin{gathered} dU(t)/dt=rU(t)(1-\kappa^{-1}U(t))-A(t)U(t)(\alpha+U(t)^2), \\ \partial_tv(t,a)+\partial_av(t,a)=-Dv(t,a), \\ a\geq 0, \quad v(t,0)=\mu A(t)U(t) \alpha+U(t)^2, \quad t ...
Liu, Zhihua, Magal, Pierre
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Bogdanov–Takens Bifurcation of a Class of Delayed Reaction–Diffusion System
International Journal of Bifurcation and Chaos, 2015In this paper, a class of reaction–diffusion system with Neumann boundary condition is considered. By analyzing the generalized eigenvector associated with zero eigenvalue, an equivalent condition for the determination of Bogdonov–Takens (B–T) singularity is obtained.
Cao, Jianzhi +3 more
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DETECTING BOGDANOV–TAKENS BIFURCATION OF TRAVELING WAVES IN REACTION–DIFFUSION SYSTEMS
International Journal of Bifurcation and Chaos, 2006In this paper we investigate the onset of instabilities in a model describing the propagation of the steady planar premixed combustion wave. In particular, we are interested in determining the Bogdanov–Takens bifurcation condition, which is investigated semi-analytically.
Gubernov, V. V. +2 more
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Invariant circles in the Bogdanov-Takens bifurcation for diffeomorphisms
Ergodic Theory and Dynamical Systems, 1996AbstractWe study a generic, real analytic unfolding of a planar diffeomorphism having a fixed point with unipotent linear part. In the analogue for vector fields an open parameter domain is known to exist, with a unique limit cycle. This domain is bounded by curves corresponding to a Hopf bifurcation and to a homoclinic connection.
Broer, H., Roussarie, R., Simó, C.
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Hopf and Bogdanov–Takens Bifurcations of a Delayed Bazykin Model
Qualitative Theory of Dynamical SystemsIn this paper, the authors investigated the Hopf and Bogdanov-Takens bifurcations of a delayed Bazykin predator-prey model with predator intraspecific interactions and ratio-dependent functional response. And they established sufficient conditions for the existence of Hopf bifurcation.
Liu, Ming +3 more
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International Journal of Biomathematics, 2020
In this paper, a neutral Hopfield neural network with bidirectional connection is considered. In the first step, by choosing the connection weights as parameters bifurcation, the critical point at which a zero root of multiplicity two occurs in the characteristic equation associated with the linearized system.
Achouri, Houssem +2 more
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In this paper, a neutral Hopfield neural network with bidirectional connection is considered. In the first step, by choosing the connection weights as parameters bifurcation, the critical point at which a zero root of multiplicity two occurs in the characteristic equation associated with the linearized system.
Achouri, Houssem +2 more
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2014
In the parameter space, curves of (classical) Poincare–Andronov–Hopf bifurcations, saddle-node bifurcations and homoclinic orbits emerge.In this chapter, we discuss the intricate patterns of heteroclinic orbits which appear near the corresponding bifurcation without parameters.
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In the parameter space, curves of (classical) Poincare–Andronov–Hopf bifurcations, saddle-node bifurcations and homoclinic orbits emerge.In this chapter, we discuss the intricate patterns of heteroclinic orbits which appear near the corresponding bifurcation without parameters.
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