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91.
We give a geometric analysis of relaxation oscillations and canard cycles in a singularly perturbed predator–prey system of Holling and Leslie types. We discuss how the canard cycles are found near the Hopf bifurcation points. The transition from small Hopf-type cycles to large relaxation cycles is also discussed. Moreover, we outline one possibility for the global dynamics. Numerical simulations are also carried out to verify the theoretical results. 相似文献
92.
Paul Bracken 《Central European Journal of Physics》2008,6(1):135-140
An effective Hamiltonian for the generalized harmonic oscillator is determined by using squeezed state wavefunctions. The
equations of motion over an extended phase space are determined and then solved perturbatively for a specific choice of the
oscillator parameters. These results are used to calculate the dynamic and geometric phases for the generalized oscillator
with this choice of parameters.
相似文献
93.
Polarization-dependent linear absorption, second-harmonic generation (SHG) and 3rd-order nonlinearities of wellaligned ZnO nanorod arrays have been investigated with ps pulses. The depressed spectral width and the enhanced intensity of reflective SHG along the long axis of ZnO nanorods were observed by using p-polarized pulses, which is explained by the optical confinements. The nonlinear absorption coefficient measured with s-polarization reached the maximum 4.0×10^4cm/GW at the wavelength -750nm, which revealed a large two-photon resonance absorption attributed to the quantum confined exciton when the polarization is vertical to the long axis of ZnO nanorod. 相似文献
94.
95.
Enhanced nonlinearity in photonic crystal fiber by germanium doping in the core region 总被引:2,自引:0,他引:2
Germanium doping in silica can be used as a method for nonlinearity enhancement.Properties of the enhanced nonlinearity in photonic crystal fiber(PCF)with a GeO2-doped core are investigated theoretically by using all-vector finite element method.Numerical result shows that the nonlinear coefficient of PCF is greatly enhanced with increasing doping concentration,furthermore,optimal radius of the doped region should be considered for the desired operating wavelength. 相似文献
96.
M.J. Kaiser 《Applied Mathematics Letters》1996,9(6):67-70
Based on Gage's notion of a “positive center” of a planar convex set, an ε-positive center figure is defined, constructed, and illustrated through example. The existence of an ε-positive center point, and the convexity of the ε-positive center figure, is conjectured. 相似文献
97.
用三次B样条函数配点法,求得在矩形波冲击下具有立方非线性产品包装的冲击谱。讨论了软、硬非线性及外界激励幅值对产品损坏边界的影响。提出用损坏边界曲面来描述非线性产品包装的安全区域,并作出了相应的损坏边界曲面. 相似文献
98.
Das R Kumar SK Kumar A 《Journal of magnetic resonance (San Diego, Calif. : 1997)》2005,177(2):318-328
Geometric phases have stimulated researchers for its potential applications in many areas of science. One of them is fault-tolerant quantum computation. A preliminary requisite of quantum computation is the implementation of controlled dynamics of qubits. In controlled dynamics, one qubit undergoes coherent evolution and acquires appropriate phase, depending on the state of other qubits. If the evolution is geometric, then the phase acquired depend only on the geometry of the path executed, and is robust against certain types of error. This phenomenon leads to an inherently fault-tolerant quantum computation. Here we suggest a technique of using non-adiabatic geometric phase for quantum computation, using selective excitation. In a two-qubit system, we selectively evolve a suitable subsystem where the control qubit is in state |1, through a closed circuit. By this evolution, the target qubit gains a phase controlled by the state of the control qubit. Using the non-adiabatic geometric phase we demonstrate implementation of Deutsch-Jozsa algorithm and Grover's search algorithm in a two-qubit system. 相似文献
99.
100.
We consider a space of Chebyshev splines whose left and right derivatives
satisfy linear constraints that are given by arbitrary nonsingular connection matrices.
We show that for almost all knot sequences such spline spaces have basis functions
whose support is equal to the support of the ordinary B-splines with the same knots.
Consequently, there are knot insertion and evaluation algorithms analogous to de Boors
algorithm for ordinary splines. 相似文献