Nonlinear Dynamics - In this paper, the current-controlled DC–DC buck converter from a new perspective are studied through the switching theory of flow, and the analytical conditions of the... 相似文献
A hyperchaotic system with an infinite line of equilibrium points is described. A criterion is proposed for quantifying the hyperchaos, and the position in the three-dimensional parameter space where the hyperchaos is largest is determined. In the vicinity of this point, different dynamics are observed including periodicity, quasi-periodicity, chaos, and hyperchaos. Under some conditions, the system has a unique bistable behavior, characterized by a symmetric pair of coexisting limit cycles that undergo period doubling, forming a symmetric pair of strange attractors that merge into a single symmetric chaotic attractor that then becomes hyperchaotic. The system was implemented as an electronic circuit whose behavior confirms the numerical predictions. 相似文献
This paper addresses a previously unexplored regime of three-dimensional dissipative chaotic flows in which all but one of the nonlinearities are quadratic. The simplest such systems are determined, and their equilibria and stability are described. These systems often have one or more infinite lines of equilibrium points and sometimes have stable equilibria that coexist with the strange attractors, which are sometimes hidden. Furthermore, the coefficient of the single nonquadratic term provides a simple means for scaling the amplitude and frequency of the system. 相似文献
By introducing a memristor into a chaotic system with a single non-quadratic term and substituting an absolute value function for conditional symmetry, a unique chaotic system is constructed. Firstly, the system shares a special structure of symmetry and conditional symmetry. Secondly, the amplitude and frequency of the system variables can be rescaled by the applied memristor. Interestingly it gives a new case of attractor control namely partial amplitude control and global frequency control. At last, as a new regime of extreme multistability, the memristive system shows relatively simple bifurcation according to the initial condition. This new class of chaotic system has never been reported to the best of our knowledge.
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
Vibration data are required for condition monitoring in machinery, and can only be collected indirectly after transferring through rods, shells, rotating shafts or other components in many engineering applications. Investigation on the transfer characteristics of vibration in these components is very helpful to guarantee the efficiency of the data collected indirectly. Here, the longitudinal wave propagation in a rod with variable cross-section is investigated. First, the equations of motion are established for the rod based upon the elementary wave theory, the Love theory and the Mindlin–Herrmann theory. Second, the transfer matrix method is employed to explore the propagation characteristics of the rod from the derived equations of motion. Finally, two kinds of rods with the cross-sections varying in the exponential and the polynomial forms are used to illustrate the analytical predictions of the propagation characteristics of the longitudinal wave, which are compared with the results from the finite element analysis (FEA) method. It is shown that Poisson's effect or the shear deformation plays a very important role in the longitudinal wave propagation in the rod and can widen the rod's stop band moderately. Moreover, the cut-off frequency of the rod is unconcerned with the variation form of the cross-section, but dependent on the area ratio between both the ends of the rod, even though Poisson's effect or shear deformation is included. 相似文献
Studies on first-passage failure are extended to the multi-degree-of-freedom quasi-non-integrable-Hamiltonian systems under
parametric excitations of Gaussian white noises in this paper. By the stochastic averaging method of energy envelope, the
system's energy can be modeled as a one-dimensional approximate diffusion process by which the classical Pontryagin equation
with suitable boundary conditions is applicable to analyzing the statistical moments of the first-passage time of an arbitrary
order. An example is studied in detail and some numerical results are given to illustrate the above procedure.
The project supported by the Post-Doctoral Foundation of China 相似文献