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71.
The dimensionless partial differential equations governing thedynamics of a thin flexible isotropic plate with an external load arederived and investigated. The period doubling bifurcations, as well asthe chaotic dynamics, are detected and analyzed. The algorithms leadingto the reduction of the original equations to those of a difference setof ordinary differential and algebraic equations are proposed, comparedto other known methods, and then applied to the problem.Among others, it is shown that, in spite of the system complexity, theFeigenbaum scenario exhibited by one-dimensional maps also governs theroute to chaos in the continuous system under consideration. 相似文献
72.
Zbigniew Jelonek 《Proceedings of the American Mathematical Society》2003,131(5):1361-1367
Let be a polynomial of degree . Assume that the set there is a sequence s.t. and is finite. We prove that the set of generalized critical values of (hence in particular the set of bifurcation points of ) has at most points. Moreover, We also compute the set effectively.
73.
74.
75.
Björn Birnir 《Journal of statistical physics》2007,128(1-2):535-568
A system of ordinary differential equations (ODEs) is derived from a discrete system of Vicsek, Czirók et al. [Phys. Rev. Lett.
75(6):1226–1229, 1995], describing the motion of a school of fish. Classes of linear and stationary solutions of the ODEs are
found and their stability explored using equivariant bifurcation theory. The existence of periodic and toroidal solutions
is also proven under deterministic perturbations and structurally stable heteroclinic connections are found. Applications
of the model to the migration of the capelin, a pelagic fish that undertakes an extensive migration in the North Atlantic,
are discussed and simulation of the ODEs presented. 相似文献
76.
David Chan 《Physica D: Nonlinear Phenomena》2007,234(2):98-104
We give a new characterisation of resonance in Hopf bifurcation from relative equilibria in systems with compact symmetry group. This characterisation provides a full geometric explanation of the resonance phenomenon. In addition, we develop techniques based on normal form theory to give a complete solution to the associated bifurcation problem. 相似文献
77.
CUI Tao TANG ShunLin ZHANG Lei & YU DaRen School of Energy Science Engineering Harbin Institute of Technology Harbin China Pharmaceutical College Heilongjiang University of Chinese Medicine Institution Harbin China 《中国科学B辑(英文版)》2011,(7)
Catalytic CO oxidation on platinum group metals exhibits nonlinear phenomena such as hysteresis and bifurcation.Elucidation of the nonlinear mechanisms is important for catalyst design and control of reaction routes.Previous studies have offered initial insights into the local bifurcation behavior of CO oxidation.However,since the bifurcation behavior of CO oxidation is determined by multiple parameters such as temperature,total flux,and CO fraction,it is difficult to predict the global bifurcation behavior... 相似文献
78.
By making use of bifurcation analysis and continuation method, the authors discuss the exact number of positive solutions for a class of perturbed equations. The nonlinearities concerned are the so-called convex-concave functions and their behaviors may be asymptotic sublinear or asymptotic linear. Moreover, precise global bifurcation diagrams are obtained. 相似文献
79.
Yan LiuKailun Li Jiazhong Zhang Hang WangLiguang Liu 《Communications in Nonlinear Science & Numerical Simulation》2012,17(8):3427-3434
By the finite element method combined with Arbitrary-Lagrangian-Eulerian (ALE) frame and explicit Characteristic Based Split Scheme (CBS), the complex flows around stationary and sinusoidal pitching airfoil are studied numerically. In particular, the static and dynamic stalls are analyzed in detail, and the natures of the static stall of NACA0012 airfoil are given from viewpoint of bifurcations. Following the bifurcation in Map, the static stall is proved to be the result from saddle-node bifurcation which involves both the hysteresis and jumping phenomena, by introducing a Map and its Floquet multiplier, which is constructed in the numerical simulation of flow field and related to the lift of the airfoil. Further, because the saddle-node bifurcation is sensitive to imperfection or perturbation, the airfoil is then subjected to a perturbation which is a kind of sinusoidal pitching oscillation, and the flow structure and aerodynamic performance are studied numerically. The results show that the large-scale flow separation at the static stall on the airfoil surface can be removed or delayed feasibly, and the ensuing lift could be enhanced significantly and also the stalling incidence could be delayed effectively. As a conclusion, it can be drawn that the proper external excitation can be considered as a powerful control strategy for the stall. As an unsteady aerodynamic behavior of high angle of attack, the dynamic stall can be investigated from viewpoint of nonlinear dynamics, and there exists a rich variety of nonlinear phenomena, which are related to the lift enhancement and drag reduction. 相似文献
80.
In this paper, we present an analysis for the class of delay differential equations with one discrete delay and the right‐hand side depending only on the past. We extend the results from paper by U. Fory? (Appl. Math. Lett. 2004; 17 (5):581–584), where the right‐hand side is a unimodal function. In the performed analysis, we state more general conditions for global stability of the positive steady state and propose some conditions for the stable Hopf bifurcation occurring when this steady state looses stability. We illustrate the analysis by biological examples coming from the population dynamics. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献