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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
Beltrami fields and knotted vortex structures in incompressible fluid flows
Bulletin of the London Mathematical Society, Volume 55, Issue 3, Page 1059-1103, June 2023., 2023 Abstract This paper gives a survey on recent results about the existence of knotted vortex structures in incompressible fluids. This includes the proof of Lord Kelvin's conjecture on the existence of knotted vortex tubes in steady Euler flows and a new probabilistic approach to address Arnold's speculation that typical Beltrami fields should exhibit ...
Alberto Enciso, Daniel Peralta‐Salas
wiley +1 more source
Mathematical Biosciences and Engineering, 2023 In this article, we will investigate a retarded van der Pol-Duffing oscillator with multiple delays. At first, we will find conditions for which Bogdanov-Takens (B-T) bifurcation occurs around the trivial equilibrium of the proposed system.
Mohammad Sajid +3 more
doaj +1 more source
Natural Exponential and Three‐Dimensional Chaotic System
Advanced Science, Volume 10, Issue 15, May 26, 2023., 2023 A novel natural exponential and three‐dimensional chaotic system with higher sensitivity to initial condition is presented. Its characterizations are revealed via various chaotic dynamic indicators. The performance evaluation through recursive and entropy study verifies the model complexity and robustness, while the feasibility of this system is ...
Shiwei Liu +4 more
wiley +1 more source
International Journal of Mechanical System Dynamics, Volume 3, Issue 1, Page 85-94, March 2023., 2023 Abstract Environmental noise can lead to complex stochastic dynamical behaviors in nonlinear systems. In this paper, a Lorenz system with the parameter region with two stable fixed points and a chaotic saddle subject to white Gaussian noise is investigated as an example.
Yong Huang
wiley +1 more source
Nine Limit Cycles in a 5-Degree Polynomials Liénard System
Complexity, 2020 In this article, we study the limit cycles in a generalized 5-degree Liénard system. The undamped system has a polycycle composed of a homoclinic loop and a heteroclinic loop.
Junning Cai, Minzhi Wei, Hongying Zhu
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Resonant Homoclinic Flips Bifurcation in Principal Eigendirections
Abstract and Applied Analysis, 2013 A codimension-4 homoclinic bifurcation with one orbit flip and one inclination flip at principal eigenvalue direction resonance is considered. By introducing a local active coordinate system in some small neighborhood of homoclinic orbit, we get the ...
Tiansi Zhang, Xiaoxin Huang, Deming Zhu
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Symmetry breaking perturbations and strange attractors [PDF]
, 1996 The asymmetrically forced, damped Duffing oscillator is introduced as a prototype model for analyzing the homoclinic tangle of symmetric dissipative systems with \textit{symmetry breaking} disturbances.
A. H. Nayfeh +37 more
core +2 more sources
Bifurcation and chaos for piecewise nonlinear roll system of rolling mill
Advances in Mechanical Engineering, 2017 A non-smooth cold roll system of rolling mill is studied to reveal the bifurcation of the piecewise-smooth and discontinuous system. To examine the influence of the parameters on the dynamics, the bifurcation diagram is constructed when it is unperturbed.
Chundi Si +3 more
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Codimension 3 bifurcation from orbit-flip homoclinic orbit of weak type
Electronic Journal of Qualitative Theory of Differential Equations, 2015 This article is devoted to the research of a new codimension 3 homoclinic orbit bifurcation, which is the orbit-flip of weak type. Such kind of homoclinic orbit is a degenerate case of the orbit-flip homoclinic orbit.
Qiuying Lu, Guifeng Deng, Hua Luo
doaj +1 more source