Trans-heteroclinic bifurcation: a novel type of catastrophic shift [PDF]
Royal Society Open Science, 2018 Global and local bifurcations are extremely important since they govern the transitions between different qualitative regimes in dynamical systems. These transitions or tipping points, which are ubiquitous in nature, can be smooth or catastrophic. Smooth
Josep Sardanyés +2 more
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Emerging criticality at bifurcation points in heteroclinic dynamics [PDF]
Physical Review Research, 2020 Heteroclinic dynamics is a suitable framework to describe transient dynamics that is characteristic for ecological as well as neural systems, in particular for cognitive processes.
Maximilian Voit +1 more
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Bifurcation analysis, modulation instability and dynamical analysis of soliton solutions for generalized (3 + 1)-dimensional nonlinear wave equation with m-fractional operator [PDF]
Scientific ReportsThis research investigates the bifurcation theory of a generalized (3 + 1)-dimensional P-type nonlinear wave equation with an M-fractional derivative (M-fGP-NWE) and develops its soliton solutions.
Mohamed S. Algolam +5 more
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Modeling, dynamical analysis and numerical simulation of a new 3D cubic Lorenz-like system [PDF]
Scientific Reports, 2023 Little seems to be considered about the globally exponentially asymptotical stability of parabolic type equilibria and the existence of heteroclinic orbits in the Lorenz-like system with high-order nonlinear terms.
Haijun Wang +3 more
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Experimental Observation of Magnetic Island Heteroclinic Bifurcation in Tokamaks.
Physical Review Letters, 2021 We report empirical observations of magnetic island heteroclinic bifurcation for the first time. This behavior is observed in interacting coupled 2/1 tearing modes in the core of a DIII-D tokamak plasma.
L. Bardoczi, T. Evans
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Bifurcations of Nontwisted Heteroclinic Loop with Resonant Eigenvalues [PDF]
The Scientific World Journal, 2014 By using the foundational solutions of the linear variational equation of the unperturbed system along the heteroclinic orbits to establish the local coordinate systems in the small tubular neighborhoods of the heteroclinic orbits, we study the ...
Yinlai Jin +5 more
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Heteroclinic Bifurcation Behaviors of a Duffing Oscillator with Delayed Feedback
Shock and Vibration, 2018 The heteroclinic bifurcation and chaos of a Duffing oscillator with forcing excitation under both delayed displacement feedback and delayed velocity feedback are studied by Melnikov method.
Shao-Fang Wen, Ju-Feng Chen, Shu-Qi Guo
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Mathematical Biosciences and Engineering, 2015 In this paper, we analyze a general predator-prey modelwith state feedback impulsive harvesting strategies in which the prey species displays a strongAllee effect.
Qizhen Xiao, Binxiang Dai
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Heteroclinic bifurcation and singularly perturbed boundary value problems
Journal of Differential Equations, 1990 A singularly perturbed boundary value problem \(\dot x=f(x,y,\epsilon),\epsilon \dot y=g(x,y,\epsilon)\) with boundary conditions \[ B_ 1(x(\omega_ 0),y(\omega_ 0),\epsilon)=0,\quad B_ 2(x(\omega_ 2+\omega),y(\omega_ 0+\omega),\epsilon)=0 \] is studied.
Xiaobiao Lin
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Persistence of the heteroclinic loop under periodic perturbation
Electronic Research Archive, 2023 We consider an autonomous ordinary differential equation that admits a heteroclinic loop. The unperturbed heteroclinic loop consists of two degenerate heteroclinic orbits $ \gamma_1 $ and $ \gamma_2 $.
Bin Long, Shanshan Xu
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