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41.
Asymptotic large- and short-time behavior of solutions of the linear dispersion equation μt = Uxxx in IR× IR+, and its (2k+l)th-order extensions are studied. Such a refined scattering is based on a "Hermitian" spectral theory for a pair {B,B*} of non self-adjoint rescaled operators 相似文献
42.
F. O. O. Wagener 《Journal of Optimization Theory and Applications》2006,128(2):261-277
The present article uses perturbation techniques to approximate the value function of an economic minimization problem for
small values of the discount rate. This can be used to obtain the approximate location of the Skiba states in the problem;
these are states for which there are two distinct optimal state trajectories, converging to different optimal steady states.
It is shown that the sets of these indifference thresholds are locally smooth manifolds. For a simple example, all relevant
quantities are computed explicitly. Moreover, the approximation can be used to obtain parameter-dependent approximations to
the indifference manifolds.
Some of the results in the present article have been presented at the Skiba Satellite Workshop of the 8th Viennese Workshop
on Optimal Control, Dynamic Games, and Nonlinear Dynamics. The
author thanks Christophe Deissenberg and three anonymous referees warmly for comments that have
helped to improve the article as well as the Netherlands Organization for Science (NWO) for financial support through the
CeNDEF Pionier Project. 相似文献
43.
Ji-caiHuang 《应用数学学报(英文版)》2005,21(1):157-176
A discrete predator-prey system with Holling type-IV functional response obtained by the Euler method is first investigated. The conditions of existence for fold bifurcation, flip bifurcation and Hopf bifurcation are derived by using the center manifold theorem and bifurcation theory. Furthermore, we give the condition for the occurrence of codimension-two bifurcation called the Bogdanov-Takens bifurcation for fixed points and present approximate expressions for saddle-node, Hopfand homoclinic bifurcation sets near the Bogdanov-Takens bifurcation point. We also show the existence of degenerated fixed point with codimension three at least. The numerical simulations, including bifurcation diagrams, phase portraits, and computation of maximum Lyapunov exponents, not only show the consistence with the theoretical analysis but also exhibit the rich and complex dynamical behaviors such as the attracting invariant circle, period-doubling bifurcation from period-2,3,4 orbits.interior crisis, intermittency mechanic, and sudden disappearance of chaotic dynamic. 相似文献
44.
Sébastien Aumaître Kirone Mallick François Pétrélis 《Journal of statistical physics》2006,123(4):909-927
A bifurcating system subject to multiplicative noise can exhibit on–off intermittency close to the instability threshold. For a canonical system, we discuss the dependence of this intermittency on the Power Spectrum Density (PSD) of the noise. Our study is based on the calculation of the Probability Density Function (PDF) of the unstable variable. We derive analytical results for some particular types of noises and interpret them in the framework of on-off intermittency. Besides, we perform a cumulant expansion (N. G. van Kampen, 24, 171 (1976).) for a random noise with arbitrary power spectrum density and we show that the intermittent regime is controlled by the ratio between the departure from the threshold and the value of the PSD of the noise at zero frequency. Our results are in agreement with numerical simulations performed with two types of random perturbations: colored Gaussian noise and deterministic fluctuations of a chaotic variable. Extensions of this study to another, more complex, system are presented and the underlying mechanisms are discussed.
PACS Number: 05.40.-a, 05.45.-a, 91.25.-r 相似文献
45.
The influence of while noise on bifurcating dynamical systems is investigated using both Fokker-Planck and functional integral methods. Noise leads to fuzzy bifurcations where physically relevant quantities become smooth functions of the bifurcation parameters. We study dynamical and probabilistic quantities, such as invariant measures, Liapunov exponents, correlation functions, and exit times. The behavior of these quantities near the deterministic bifurcation point changes for distinct values of the control parameter. Therefore the very concept of bifurcation point becomes meaningless and must be replaced by the notion of bifurcation region. 相似文献
46.
Hopf bifurcation analysis of a density predator-prey model with crowley-martin functional response and two time delays
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In this paper, a delayed density dependent predator-prey model with Crowley-Martin functional response and two time delays for the predator is considered. By analyzing the corresponding characteristic equations, the local stability of each of the feasible equilibria of the system is addressed and the existence of Hopf bifurcation at the coexistence equilibrium is established. With the help of normal form method and center manifold theorem, some explicit formulas determining the direction of Hopf bifurcation and the stability of bifurcating period solutions are derived. Finally, numerical simulations are given to illustrate the theoretical results. 相似文献
47.
Sarker Md. Sohel Rana 《Journal of Applied Analysis & Computation》2019,9(1):31-44
We investigate the dynamics of a discrete-time predator-prey system of Leslie type. We show algebraically that the system passes through a flip bifurcation and a Neimark-Sacker bifurcation in the interior of $\R^{2}_+$ using center manifold theorem and bifurcation theory. Numerical simulations are implimented not only to validate theoretical analysis but also exhibits chaotic behaviors, including phase portraits, period-11 orbits, invariant closed circle, and attracting chaotic sets. Furthermore, we compute Lyapunov exponents and fractal dimension numerically to justify the chaotic behaviors of the system. Finally, a state feedback control method is applied to stabilize the chaotic orbits at an unstable fixed point. 相似文献
48.
49.
K. Green 《Journal of Computational and Applied Mathematics》2010,233(9):2405-2412
In this paper we consider a generic differential equation with a cubic nonlinearity and delay. This system, in the absence of delay, is known to undergo an oscillatory instability. The addition of the delay is shown to result in the creation of a number of periodic solutions with constant amplitude and a constant frequency; the number of solutions increases with the size of the delay. Indeed, for many physical applications in which oscillatory instabilities are induced by a delayed response or feedback mechanism, the system under consideration forms the underlying backbone for a mathematical model. Our study showcases the effectiveness of performing a numerical bifurcation analysis, alongside the use of analytical and geometrical arguments, in investigating systems with delay. We identify curves of codimension-one bifurcations of periodic solutions. We show how these curves interact via codimension-two bifurcation points: double singularities which organise the bifurcations and dynamics in their local vicinity. 相似文献
50.