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1.
A kind of 2-dimensional neural network model with delay is considered. By analyzing the distribution of the roots of the characteristic
equation associated with the model, a bifurcation diagram was drawn in an appropriate parameter plane. It is found that a
line is a pitchfork bifurcation curve. Further more, the stability of each fixed point and existence of Hopf bifurcation were
obtained. Finally, the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions were determined
by using the normal form method and centre manifold theory.
Foundation item: the National Natural Science, Foundation of China (19831030)
Biography: WEI Jun-jie, Professor, Doctor, E-mail: weijj@hit.edu.cn 相似文献
2.
Hopf bifurcation of an oscillator with quadratic and cubic nonlinearities and with delayed velocity feedback 总被引:2,自引:0,他引:2
This paper studies the local dynamics of an SDOF system with quadratic and cubic stiffness terms, and with linear delayed
velocity feedback. The analysis indicates that for a sufficiently large velocity feedback gain, the equilibrium of the system
may undergo a number of stability switches with an increase of time delay, and then becomes unstable forever. At each critical
value of time delay for which the system changes its stability, a generic Hopf bifurcation occurs and a periodic motion emerges
in a one-sided neighbourhood of the critical time delay. The method of Fredholm alternative is applied to determine the bifurcating
periodic motions and their stability. It stresses on the effect of the system parameters on the stable regions and the amplitudes
of the bifurcating periodic solutions.
The project supported by the National Natural Science Foundation of China (19972025) 相似文献
3.
The bifurcation dynamics of shallow arch which possesses initial deflection under periodic excitation for the case of 1∶2
internal resonance is studied in this paper. The whole parametric plane is divided into several different regions according
to the types of motions; then the distribution of steady state motions of shallow arch on the plane of physical parameters
is obtained. Combining with numerical method, the dynamics of the system in different regions, especially in the Hopf bifurcation
region, is studied in detail. The rule of the mode interaction and the route to chaos of the system is also analysed at the
end.
Project supported by National Natural Science Foundation and National Youth Science Foundation of China 相似文献
4.
Periodic vibro-impacts and their stability of a dual component system 总被引:11,自引:0,他引:11
The coexisting periodic impacting motions and their multiplicity of a kind of dual component systems under harmonic excitation
are analytically derived. The stability condition of a periodic impacting motion is given by analyzing the propagation of
small, arbitrary perturbation from that motion. In numerical simulations, the periodic impacting motions are classified according
to the system states before and after an impact. The numerical results show that there exist many types of vibro-impacts and
the bifurcation of periodic vibro-impacts is not smooth.
Project supported in part by National Natural Science Foundation of China under the grant 59572024 and in part by Trans-century
Training Program Foundation for the Talents by the State Education Commission of China 相似文献
5.
Bifurcation of the electromechanically coupled subsynchronous torsional oscillating system with hysteretic behavior 总被引:1,自引:0,他引:1
In subsynchronous resonance (SSR) systems where shaft systems of turbine-generator sets are coupling with electric networks,
Hopf bifurcation will occur under certain conditions. Some singularity phenomena may generate when the hysteretic behavior
of couplings in the shaft systems in considered. In this paper, the intrinsic multiple-scale harmonic balance method is extended
to the nonlinear autonomous system with the non-analytic property, and the dynamic complexities of the system near the Hopf
bifurcation point are analyzed.
The project supported by the National Natural Science Foundation of China (as a key project) and the State Education Committee
Pre-research Foundation. 相似文献
6.
This paper studies interactions of pipe and fluid and deals with bifurcations of a cantilevered pipe conveying a steady fluid,
clamped at one end and having a nozzle subjected to nonlinear constraints at the free end. Either the nozzle parameter or
the flow velocity is taken as a variable parameter. The discrete equations of the system are obtained by the Ritz-Galerkin
method. The static stability is studied by the Routh criteria. The method of averaging is employed to examine the analytical
results and the chaotic motions. Three critical values are given. The first one makes the system lose the static stability
by pitchfork bifurcation. The second one makes the system lose the dynamical stability by Hopf bifurcation. The third one
makes the periodic motions of the system lose the stability by doubling-period bifurcation.
The project supported by the Science Foundation of Tongji University and Tongji University and National Key Projects of China
under Grant No. PD9521907. 相似文献
7.
This paper presents several sufficient conditions for the existence and attractivity of almost periodic solution for a new class of recurrent neural networks with unbounded delays and variable coefficients. Different from the normal approach, that's to say, without resorting to any Lyapunov function, these results are obtained by utilizing generalized Halanay inequality technique and combining the theory of exponential dichotomy with fixed point method. Some existing results are found to be special case of this paper. In addition, the exponential stability of the almost periodic solution, which is not studied in the earlier references, is also considered for the system. An example is given to illustrate the feasibility of our results.This work was jointly supported by the National Natural Science Foundation of China under Grant 60373067, the Hong Kong Special Administrative Region, China with Project No. 7001146, the Natural Science Foundation of Jiangsu Province, China under Grant BK2003053, Qing-Lan Engineering Project of Jiangsu Province, China. 相似文献
8.
Codimension two bifurcation of a vibro-bounce system 总被引:1,自引:0,他引:1
A three-degree-of-freedom vibro-bounce system is considered. The disturbed map of period one single-impact motion is derived analytically. A center manifold theorem technique is applied to reduce the Poincaré map to a three-dimensional one, and the normal form map associated with Hopf-flip bifurcation is obtained. Dynamical behavior of the system, near the point of codimension two bifurcation, is investigated by using qualitative analysis and numerical simulation. It is found that near the point of Hopf-flip bifurcation there exists not only Hopf bifurcation of period one single-impact motion, but also Hopf bifurcation of period two double-impact motion. The results from simulation show that there exists an interesting torus doubling bifurcation near the codimension two bifurcation. The torus doubling bifurcation makes the quasi-periodic attractor associated with period one single-impact motion transform to the other quasi-periodic attractor represented by two attracting closed circles. The torus bifurcation is qualitatively different from the typical torus doubling bifurcation occurring in the vibro-impact systems. Different routes from period one single-impact motion to chaos are observed by numerical simulation.The project supported by the National Natural Science Foundation of China (10172042, 50475109) and the Natural Science Foundation of Gansu Province Government of China (ZS-031-A25-007-Z (key item)) 相似文献
9.
陆启韶 《应用数学和力学(英文版)》1987,8(11):1045-1056
A more general kind of nonlinear evolution equations with integral operators is discussed in order to study the spatially
periodic static bifurcating solutions and their stability. At first, the necessary condition and the sufficient condition
for the existence of bifurcation are studied respectively. The stability of the equilibrium solutions is analyzed by the method
of semigroups of linear operators. We also obtain the principle of exchange of stability in this case. As an example of application,
a concrete result for a special case with integral operators of exponential type is presented.
This work was supported by the Chinese National Foundation of Natural Science 相似文献
10.
甘春标 《Acta Mechanica Sinica》2004,20(5):558-566
A new procedure is developed to study the stochastic Hopf bifurcation in quasiintegrable-Hamiltonian systems under the Gaussian white noise excitation. Firstly, the singular boundaries of the first-class and their asymptotic stable conditions in probability are given for the averaged Ito differential equations about all the sub-system‘s energy levels with respect to the stochastic averaging method. Secondly, the stochastic Hopf bifurcation for the coupled sub-systems are discussed by defining a suitable bounded torus region in the space of the energy levels and employing the theory of the torus region when the singular boundaries turn into the unstable ones. Lastly, a quasi-integrable-Hamiltonian system with two degrees of freedom is studied in detail to illustrate the above procedure.Moreover, simulations by the Monte-Carlo method are performed for the illustrative example to verify the proposed procedure. It is shown that the attenuation motions and the stochastic Hopf bifurcation of two oscillators and the stochastic Hopf bifurcation of a single oscillator may occur in the system for some system‘s parameters. Therefore, one can see that the numerical results are consistent with the theoretical predictions. 相似文献
11.
The cavitated bifurcation problem in a solid sphere composed of two compressible hyper-elastic materials is examined. The
bifurcation solution for the composed sphere under a uniform radial tensile boundary dead-load is obtained. The bifurcation
curves and the stress contributions subsequent to the cavitation are given. The right and left bifurcation as well as the
catastrophe and concentration of stresses are analyzed. The stability of solutions is discussed through an energy comparison.
Project supported by the National Natural Science Foundation of China (No. 19802012). 相似文献
12.
This paper shows the mechanism of instability and chaos in a cantilevered pipe conveying steady fluid. The pipe under consideration
has added mass or a nozzle at the free end. The Galerkin method is used to transform the original system into a set of ordinary
differential equations and the standard methods of analysis of the discrete system are introduced to deal with the instability.
With either the nozzle parameter or the flow velocity increasing, a route to chaos can be observed very clearly: the pipe
undergoing buckling (pitchfork bifurcation), flutter (Hopf bifurcation), doubling periodic motion (pitchfork bifurcation)
and chaotic motion occurring finally.
The project supported by the National Key Projects of China under grant No. PD9521907 and Science Foundation of Tongji University
under grant No. 1300104010. 相似文献
13.
The Hopfbifurcation for the Brusselator ordinary-differential-equation (ODE) model and the corresponding partial-differential-equation (PDE) model are investigated by using the Hopf bifurcation theorem. The stability of the Hopf bifurcation periodic solution is discussed by applying the normal form theory and the center manifold theorem. When parameters satisfy some conditions, the spatial homogenous equilibrium solution and the spatial homogenous periodic solution become unstable. Our results show that if parameters are properly chosen, Hopf bifurcation does not occur for the ODE system, but occurs for the PDE system. 相似文献
14.
In this paper, we consider the effect of distributed delays in a three-neuron unidirectional ring. Sufficient conditions for existence of unique equilibrium, multiple equilibria and their local stability are derived. Taking the average delay as a bifurcation parameter, we find two critical values at which the system undergoes Hopf bifurcations. The orbital asymptotic stability of the Hopf bifurcating periodic solutions is investigated by using the method of multiple scales. The global Hopf bifurcation is also studied. Finally, the theoretical results are illustrated by some numerical simulations. 相似文献
15.
Hopf Bifurcation on a Two-Neuron System with Distributed Delays: A Frequency Domain Approach 总被引:1,自引:0,他引:1
In this paper, a more general two-neuron model with distributed delays and weak kernel is investigated. By applying the frequency domain approach and analyzing the associated characteristic equation, the existence of bifurcation parameter point is determined. Furthermore, we found that if the mean delay is used as a bifurcation parameter, Hopf bifurcation occurs for the weak kernel. This means that a family of periodic solutions bifurcates from the equilibrium when the bifurcation parameter exceeds a critical value. The direction and stability of the bifurcating periodic solutions are determine by the Nyquist criterion and the graphical Hopf bifurcation theorem. Some numerical simulations for justifying the theoretical analysis are also given. 相似文献
16.
Codimension two bifurcation and chaos of a vibro-impact forming machine associated with 1:2 resonance case 总被引:1,自引:0,他引:1
A vibro-impact forming machine with double masses is considered. The components of the vibrating system collide with each
other. Such models play an important role in the studies of dynamics of mechanical systems with impacting components. The
Poincaré section associated with the state of the impact-forming system, just immediately after the impact, is chosen, and
the period n single-impact motion and its disturbed map are derived analytically. A center manifold theorem technique is applied to reduce
the Poincaré map to a two-dimensional map, and the normal form map associated with codimension two bifurcation of 1:2 resonance
is obtained. Unfolding of the normal form map is analyzed. Dynamical behavior of the impact-forming system, near the point
of codimension two bifurcation, is investigated by using qualitative analyses and numerical simulation. Near the point of
codimension two bifurcation there exists not only Neimark-Sacker bifurcation associated with period one single-impact motion,
but also Neimark-Sacker bifurcation of period two double-impact motion. Transition of different forms of fixed points of single-impact
periodic orbits, near the bifurcation point, is demonstrated, and different routes from periodic impact motions to chaos are
also discussed.
The project supported by the National Natural Science Foundation of China (10572055, 50475109) and the Natural Science Foundation
of Gansu Province Government of China (3ZS051-A25-030(key item)) The English text was polished by Keren Wang. 相似文献
17.
The topological bifurcation diagrams and the coefficients of bifurcation equation were obtained by C-L method. According to obtained bifurcation diagrams and combining control theory, the method of robust control of periodic bifurcation was presented, which differs from generic methods of bifurcation control. It can make the existing motion pattern into the goal motion pattern. Because the method does not make strict requirement about parametric values of the controller, it is convenient to design and make it. Numerical simulations verify validity of the method. 相似文献
18.
IntroductionRotor-bearings systems applied widely in industry are nonlinear dynamic systems of multi-degree-of-freedom.Synchronous vibration is its typical motion under unavoidable unbalance.Subharmonic,quasi-periodic and chaotic vibrations,caused by the … 相似文献
19.
Since the ratio-dependent theory reflects the fact that predators must share and compete for food, it is suitable for describing the relationship between predators and their preys and has recently become a very important theory put forward by biologists. In order to investigate the dynamical relationship between predators and their preys, a so-called Michaelis-Menten ratio-dependent predator-prey model is studied in this paper with gestation time delays of predators and preys taken into consideration. The stability of the positive equilibrium is investigated by the Nyquist criteria, and the existence of the local Hopf bifurcation is analyzed by employing the theory of Hopf bifurcation. By means of the center manifold and the normal form theories, explicit formulae are derived to determine the stability, direction and other properties of bifurcating periodic solutions. The above theoretical results are validated by numerical simulations with the help of dynamical software WinPP. The results show that if both the gestation delays are small enough, their sizes will keep stable in the long run, but if the gestation delays of predators are big enough, their sizes will periodically fluc-tuate in the long term. In order to reveal the effects of time delays on the ratio-dependent predator-prey model, a ratiodependent predator-prey model without time delays is considered. By Hurwitz criteria, the local stability of positive equilibrium of this model is investigated. The conditions under which the positive equilibrium is locally asymptotically stable are obtained. By comparing the results with those of the model with time delays, it shows that the dynamical behaviors of ratio-dependent predator-prey model with time delays are more complicated. Under the same conditions, namely, with the same parameters, the stability of positive equilibrium of ratio-dependent predator-prey model would change due to the introduction of gestation time delays for predators and preys. Moreover, with the variation of time delays, the positive equilibrium of the ratio-dependent predator-prey model subjects to Hopf bifurcation. 相似文献
20.
This paper presents a detailed analysis on the dynamics of a ring network with small world connection. On the basis of Lyapunov stability approach, the asymptotic stability of the trivial equilibrium is first investigated and the delay-dependent criteria ensuring global stability are obtained. The existence of Hopf bifurcation and the stability of periodic solutions bifurcating from the trivial equilibrium are then analyzed. Further studies are paid to the effects of small world connection on the stability interval and the stability of periodic solution. In particular, some complex dynamical phenomena due to short-cut strength are observed numerically, such as: period-doubling bifurcation and torus breaking to chaos, the coexistence of multiple periodic solutions, multiple quasi-periodic solutions, and multiple chaotic attractors. The studies show that small world connection may be used as a simple but efficient “switch” to control the dynamics of a system. 相似文献