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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On the Butterfly Catastrophe Model and Stability of Finite Periodic Solutions for Some Non-Linear Differential Equations [PDF]
Kirkuk Journal of Science, 2023 In this work, we find the results for the folded part projection of the butterfly catastrophe model onto the control space, using methods from catastrophe theory to obtain stability and the catastrophic behavior of finite periodic solutions for some non ...
Isam R. Faeq
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The saddle-node Hopf bifurcation with global reinjection [PDF]
, 2003 A simultaneous saddle-node and Hopf bifurcation is a basic codimension-two local bifurcation of vector fields with a phase space of dimension at least three.
Oldeman, BE +3 more
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The geometry of quadratic polynomial differential systems with a finite and an infinite saddle-node (A,B) [PDF]
, 2013 The goal is to make a global study of the family QsnSN of all real quadratic polynomial differential systems which have a finite semi-elemental saddle-node and an infinite saddle-node formed by the collision of two infinite singular points.
Oliveira, Regilene D. S. +6 more
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The Local Bifurcation of Food web Prey-Predator Model involving fear and anti-Predator behavior
Ibn Al-Haitham Journal for Pure and Applied SciencesIn this paper, the conditions under which the occurrence of the local bifurcation (such as saddle-node (SN), transcritical (TC), and pitchfork (PT)) of all stable points of a food web model have been investigated.
Hanna Rasool Hadi, Azhar Abbas Majeed
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Modeling and Analyzing the Influence of Fear on the Harvested Modified Leslie-Gower Model
مجلة بغداد للعلوم, 2023 A modified Leslie-Gower predator-prey model with a Beddington-DeAngelis functional response is proposed and studied. The purpose is to examine the effects of fear and quadratic fixed effort harvesting on the system's dynamic behavior.
Abdul Rahman Mahmoud Jamil +1 more
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Numerical continuation of canard orbits in slow-fast dynamical systems [PDF]
, 2009 A trajectory of a system with two clearly separated time scales generally consists of fast segments (or jumps) followed by slow segments where the trajectory follows an attracting part of a slow manifold. The switch back to fast dynamics typically occurs
Desroches, MF, Osinga, HM, Krauskopf, B
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Quadratic Differential Systems with a Finite Saddle-Node and an Infinite Saddle-Node (1, 1) SN-(B) [PDF]
, 2021 This paper presents a global study of the class QsnSN11 of all real quadratic polynomial differential systems which have a finite semi-elemental saddle-node and an infinite saddle-node formed by the coalescence of a finite singularity and an infinite ...
Artés Ferragud, Joan Carles +2 more
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A Fold Bifurcation Theorem of Degenerate Solutions in a Perturbed Nonlinear Equation
Abstract and Applied Analysis, 2011 We consider a nonlinear equation F(ε,λ,u)=0, where the parameter ε is a perturbation parameter, F is a differentiable mapping from R×R×X to Y, and X, Y are Banach spaces.
Ping Liu, Yuwen Wang
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Hopf-zero bifurcation of Oregonator oscillator with delay
Advances in Difference Equations, 2018 In this paper, we study the Hopf-zero bifurcation of Oregonator oscillator with delay. The interaction coefficient and time delay are taken as two bifurcation parameters. Firstly, we get the normal form by performing a center manifold reduction and using
Yuting Cai, Liqin Liu, Chunrui Zhang
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