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Hopf bifurcation from a turning point. [PDF]
Journal für die reine und angewandte Mathematik (Crelles Journal), 1985 The classical Hopf bifurcation theorem proves the bifurcation of periodic solutions from a branch of steady states for ODE's (or some types of parabolic PDE's) depending on one real parameter if (i) this branch can be parameterized over this parameter set and (ii) if the dimension of the unstable manifold of the steady states changes at a certain ...
Lauterbach, R., Lauterbach, Reiner
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Multiple limit point bifurcation
Journal of Mathematical Analysis and Applications, 1980 In this paper we present a new bifurcation or branching phenomenon which we call multiple limit point bifurcation. It is of course well known that bifurcation points of some nonlinear functional equation G(u, λ) = 0 are solutions (u_0, λ_0) at which two distinct smooth branches of solutions, say [u(e), λ(e)] and [u^(e), λ^(e)], intersect ...
Decker, Dwight W., Keller, Herbert B.
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Cluster Oscillation of a Fractional-Order Duffing System with Slow Variable Parameter Excitation
Fractal and Fractional, 2022 The complicated dynamic behavior of a fractional-order Duffing system with slow variable parameter excitation is investigated. The stability and bifurcation behavior of the fast subsystem are analyzed by using the dynamic theory of fractional-order ...
Xianghong Li, Yanli Wang, Yongjun Shen
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Optimization of Hopf Bifurcation Points
SIAM Journal on Scientific Computing, 2023 We introduce a numerical technique for controlling the location and stability properties of Hopf bifurcations in dynamical systems. The algorithm consists of solving an optimization problem constrained by an extended system of nonlinear partial differential equations that characterizes Hopf bifurcation points.
Nicolas Boullé +2 more
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Frontiers in Materials, 2022 The arch is a common structural form in bridge engineering; its collapse is often caused by instability. In this article, in-plane nonlinear instability of pin-ended functionally graded material (FGM) arches with two cross-sectional types under local ...
Jinman Zhou +5 more
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Mathematics, 2020 Bifurcations have been studied with an extensive analysis of boundary curves of red, fixed components in the parametric space for a uniparametric family of simple-root finders under the Möbius conjugacy map applied to a quadratic polynomial.
Min-Young Lee, Young Ik Kim
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Hopf bifurcation analysis of Sel’kov model with time delay
Xi'an Gongcheng Daxue xuebao, 2023 The Sel’kov model with time-delay diffusion under homogeneous Neumann boundary conditions is considered. Firstly, the local asymptotically stability of the positive equilibrium point of the model is obtained by using spectral theory.
MA Yani, YUAN Hailong, WANG Yadi
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Complex Dynamics of a Predator-Prey System With Gompertz Growth and Herd Behavior
International Journal of Analysis and Applications, 2023 The complex dynamics of a predator-prey system in discrete time are studied. In this system, we consider the prey’s Gompertz growth and the square-root functional response. The existence of fixed points and stability are examined.
Rizwan Ahmed, M. B. Almatrafi
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Stability and Hopf bifurcation on an SEIR delayed model with logistic growth [PDF]
Songklanakarin Journal of Science and Technology (SJST), 2018 This paper investigates the stability and Hopf bifurcation of SEIR delay model with logistic growth. Firstly, the existence and uniqueness of equilibrium point are analyzed.
Aekabut Sirijampa +2 more
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Relaxation to Fixed Points in the Logistic and Cubic Maps: Analytical and Numerical Investigation
Entropy, 2013 Convergence to a period one fixed point is investigated for both logistic and cubic maps. For the logistic map the relaxation to the fixed point is considered near a transcritical bifurcation while for the cubic map it is near a pitchfork bifurcation. We
Edson D. Leonel +2 more
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