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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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Bifurcation from a Heteroclinic Solution in Differential Delay Equations [PDF]
Transactions of the American Mathematical Society, 1985 Consider differential delay equations \(\dot x(\)t)\(=af(x(t-1))\) with periodic nonlinearity \(f: R\to R\) of class \(C^ 1\) and parameter \(a>0\). First, we prove that - under additional assumptions on the graph of f - there exists a parameter \(a_ 0\) with a heteroclinic solution connecting the equilibria given by zeros \(A0\) of f, where B-A is the
Walther, Hans-Otto +1 more
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Pitchfork bifurcation and heteroclinic connections in the Kuramoto–Sivashinsky PDE
Journal of Computational DynamicsWe present a method for the complete analysis of the dynamics of dissipative Partial Differential Equations (PDEs) undergoing a pitchfork bifurcation. We apply our technique to the Kuramoto--Sivashinsky PDE on the line to obtain a computer-assisted proof of the creation of two symmetric branches of non-symmetric fixed points and heteroclinic ...
Kubica, Jacek +2 more
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Homoclinic and heteroclinic bifurcations in a two-dimensional endomorphism
Facta universitatis - series: Electronics and Energetics, 2003 Our study concerns global bifurcations occurring in noninvertible maps, it consists to show that there exists a link between contact bifurcations of a chaotic attractor and homoclinic bifurcations of a saddle point or a saddle cycle being on the boundary of the chaotic attractor.
Ilham Djellit, Mohamed R. Ferchichi
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Asymptotic Expansion of the Heteroclinic Bifurcation for the Planar Normal Form of the 1:2 Resonance [PDF]
International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 2016 Luci Any Roberto +2 more
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, 2019 In the last few years, Battelli and Feckan have developed a functional analytic method to rigorously prove the existence of chaotic behaviors in time-perturbed piecewise smooth systems whose unperturbed part has a piecewise continuous homoclinic solution.
Yurong Li, Zhengdong Du
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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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Bifurcations of heteroclinic loops with nonresonant eigenvalues
Journal of Mathematics and Computer Science, 2017 Dandan Xie +3 more
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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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Energy Science &Engineering, Volume 11, Issue 12, Page 4666-4686, December 2023., 2023 Aiming at the issue of torsional vibration characteristics analysis of wind turbine drivetrain, a mathematical model is established by considering electromechanical coupling effect. And a generalized Hamiltonian function can be used for Homoclinic or Heteroclinic bifurcation analysis.
Jianxiang Yang +5 more
wiley +1 more source