Results 31 to 40 of about 7,371 (144)
Mathematical Biosciences and Engineering, 2023 In this paper, we consider the dynamics of a slow-fast Bazykin's model with piecewise-smooth Holling type Ⅰ functional response. We show that the model has Saddle-node bifurcation and Boundary equilibrium bifurcation.
Xiao Wu, Shuying Lu , Feng Xie
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An example of bifurcation to homoclinic orbits
Journal of Differential Equations, 1980 AbstractConsider the equation ẍ − x + x2 = −λ1x + λ2ƒ(t) where ƒ(t + 1) = ƒ(t) and λ = (λ1, λ2) is small. For λ = 0, there is a homoclinic orbit Γ through zero. For λ ≠ 0 and small, there can be “strange” attractors near Γ. The purpose of this paper is to determine the curves in λ-space of bifurcation to “strange” attractors and to relate this to ...
Shui-Nee Chow +2 more
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The Twisting Bifurcations of Double Homoclinic Loops with Resonant Eigenvalues
Abstract and Applied Analysis, 2013 The twisting bifurcations of double homoclinic loops with resonant eigenvalues are investigated in four-dimensional systems. The coexistence or noncoexistence of large 1-homoclinic orbit and large 1-periodic orbit near double homoclinic loops is given ...
Xiaodong Li +3 more
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Physics Open, 2021 We consider the dynamics of a particle inside the metastable well of a cubic potential. In the classical picture the particle can oscillate inside the well when its total energy is less than a critical value Ec at which point a homoclinic bifurcation ...
Akshay Pal, Jayanta K. Bhattacharjee
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Bifurcation of an Orbit Homoclinic to a Hyperbolic Saddle of a Vector Field in R4
Discrete Dynamics in Nature and Society, 2015 We perform a bifurcation analysis of an orbit homoclinic to a hyperbolic saddle of a vector field in R4. We give an expression of the gap between returning points in a transverse section by renormalizing system, through which we find the existence of ...
Tiansi Zhang, Dianli Zhao
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Complex Behaviors of Epidemic Model with Nonlinear Rewiring Rate
Complexity, 2020 An SIS propagation model with the nonlinear rewiring rate on an adaptive network is considered. It is found by bifurcation analysis that the model has the complex behaviors which include the transcritical bifurcation, saddle-node bifurcation, Hopf ...
Ding Fang, Yongxin Zhang, Wendi Wang
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Bifurcation of homoclinics of Hamiltonian systems [PDF]
Proceedings of the American Mathematical Society, 2008 We obtain sufficient conditions for bifurcation of homoclinic trajectories of nonautonomous Hamiltonian vector fields parametrized by a circle, together with estimates for the number of bifurcation points in terms of the Maslov index of the asymptotic stable and unstable bundles of the linearization at the stationary branch.
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Bifurcation and Chaos Prediction in Nonlinear Gear Systems
Shock and Vibration, 2014 The homoclinic bifurcation and transition to chaos in gear systems are studied both analytically and numerically. Applying Melnikov analytical method, the threshold values for the occurrence of chaotic motion are obtained.
Anooshirvan Farshidianfar, Amin Saghafi
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Homoclinic Orbits In Slowly Varying Oscillators [PDF]
, 1987 We obtain existence and bifurcation theorems for homoclinic orbits in three-dimensional flows that are perturbations of families of planar Hamiltonian systems. The perturbations may or may not depend explicitly on time.
Holmes, Philip, Wiggins, Stephen
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A NUMERICAL TOOLBOX FOR HOMOCLINIC BIFURCATION ANALYSIS [PDF]
International Journal of Bifurcation and Chaos, 1996 This paper presents extensions and improvements of recently developed algorithms for the numerical analysis of orbits homoclinic to equilibria in ODEs and describes the implementation of these algorithms within the standard continuation package AUTO86.
Yu. A. Kuznetsov +3 more
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