共查询到20条相似文献,搜索用时 62 毫秒
1.
This paper studies systematically a Bedd-ington?CDeAngelis prey?Cpredator system with harvesting and impulsive state feedback control. Conditions for existence and stability of predator-free periodic solution are obtained. When the predator-free periodic solution loses its stability, the existence and stability of nontrivial period solution are also established. Furthermore, computer simulations show that this impulsive system displays a series of complex phenomena, including period-doubling bifurcation and cascade, period window, and chaotic bands. Through numerical simulation, it is also observed that capture capability can influence the amount of predator released and the interval of the stability for nontrivial period-1 solution. Moreover, the superiority of impulsive state feedback control strategy is also exhibited over the impulsive fixed-time control. 相似文献
2.
Zakaria Belhachmi Christine Bernardi Andreas Karageorghis 《Journal of Mathematical Fluid Mechanics》2004,6(2):121-156
This paper deals with the spectral element discretization
of the Navier-Stokes equations in a disk with discontinuous
boundary data, which is known as the driven cavity problem.
The numerical treatment does not involve any
regularization of these data. Relying on a variational
formulation in the primitive variables of
velocity and pressure, we describe a discretization of these equations and
derive error estimates in appropriate weighted Sobolev spaces.
We propose an algorithm to solve the
nonlinear discrete system and present numerical experiments to verify its
efficiency. 相似文献
3.
In this paper, we consider a variable yield model of a single-species growth in a well-stirred tank containing fresh medium, assuming the instances of time as triggering factors in which the nutrient refilling process and the removal of microorganisms by the uptake of lethal external antibiotic are initiated. It is also assumed that the periodic nutrient refilling and the periodic antibiotic injection occur with the same periodicity, but not simultaneously. The model is then formulated in terms of autonomous differential equations subject to impulsive perturbations. It is observed that either the population of microorganisms essentially washes out, or more favorably, the system is permanent. To describe this dichotomy, some biologically significant integral conditions are introduced. Further, it is shown that in a certain critical situation, a nontriviai periodic solution emerges via a bifurcation phenomenon. Finally, the dynamics of the model is illustrated with numerical experiments and computer simulations. 相似文献
4.
In supercritical regime, the coupled model equations for the axially moving beam with simple support boundary conditions are considered. The critical speed is determined by linear bifurcation analysis, which is in agreement with the results in the literature. For the corresponding static equilibrium state, the second-order asymptotic nontrivial solutions are obtained through the multiple scales method. Meantime, the numerical solutions are also obtained based on the finite difference method. Comparisons among the analytical solutions, numerical solutions and solutions of integro-partial-differential equation of transverse which is deduced from coupled model equations are made. We find that the second-order asymptotic analytical solutions can well capture the nontrivial equilibrium state regardless of the amplitude of transverse displacement. However, the integro-partial-differential equation is only valid for the weak small-amplitude vibration axially moving slender beams. 相似文献
5.
Steady-state responses and their stability of nonlinear vibration of an axially accelerating string 总被引:1,自引:1,他引:0
The steady-state transverse vibration of an axtally movmg strmg wtm geometric nonlinearity was investigated. The transport speed was assumed to be a constant mean speed with small harmonic variations, The nonlinear partial-differential equation that governs the transverse vibration of the string was derived by use of the Hamilton principle. The method of multiple scales was applied directly to the equation. The solvability condition of eliminating the secular terms was established, Closed form solutions for the amplitude and the existence conditions of nontrivial steady-state response of the two-to-one parametricresonance were obtained. Some numerical examples showing effects of the mean .transport speed, the amplitude and the frequency of speed variation were presented. The Liapunov linearized stability theory was employed to derive the instability conditions of the trivial solution and the nontrivial solutions for the two-to-one parametric resonance. Some numerical examples highlighting influences of the related parameters on the instability conditions were presented. 相似文献
6.
This paper presents a contribution to level‐set reinitialization in the context of discontinuous Galerkin finite element methods. We focus on high‐order polynomials for the discretization and level set geometries, which are comparable to the element size. In contrast to hyperbolic and geometric reinitialization techniques, our method relies on solving a nonlinear elliptic PDE iteratively. We critically compare two different variants of the algorithm experimentally in numerical studies. The results demonstrate that the method is stable for nontrivial test cases and shows high‐order accuracy. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
7.
In nonlinear elasticity the exact geometry of deformation is combined with general constitutive relations. This allows a very sophisticated interaction of deformations in different material directions. Based on the Cosserat theory for planar deformations of nonlinearly elastic rods we demonstrate some paradoxical bending effects caused by a nontrivial interaction of extension, flexure, and shear. The analytical results are illustrated by numerical examples. 相似文献
8.
9.
10.
11.
Thin triangular blunt-nosed plate in a viscous hypersonic flow 总被引:1,自引:0,他引:1
The effect of a small blunt nose on the hypersonic flow past a thin, high-sweep and high-aspect-ratio plate at small incidence
is investigated. The analysis is made by means of numerical simulation within the framework of the parabolized Navier-Stokes
equations and the Euler equations in combination with approximate methods for calculating the heat transfer. The results are
compared with the data of experiments in which some nontrivial features of the heat flux distributions over the thin plate
surface were revealed. 相似文献
12.
《European Journal of Mechanics - A/Solids》2007,26(3):474-490
The dynamics of systems with a finite number of degrees of freedom and nontrivial inertia matrix which are submitted to a single perfect purely inelastic unilateral constraint is studied. By adopting the measure differential formulation of J.J. Moreau, a velocity-based time-stepping method is developed, reminiscent of the catching-up algorithm for sweeping processes. It is shown that the numerical solutions converge to a solution of the problem, under a weaker assumption on the constraint as compared to position-based methods. 相似文献
13.
Response of two-degrees-of-freedom nonlinearsystem to narrow-band random parametric excitation isinvestigated. The method of multiple scales is used todetermine the equations of modulation of amplitude andphase. The effect of detunings and amplitude areanalyzed. Theoretical analyses and numerical simulationsshow that the nontrivial steady-state solution may changeform a limit cycle to a diffused limit cycle as theintensity of the random excitation increase. Under someconditions, the system may have two steady-statesolutions. 相似文献
14.
Sebastian Bönisch Vincent Heuveline Peter Wittwer 《Journal of Mathematical Fluid Mechanics》2008,10(1):45-70
We consider the problem of solving numerically the stationary incompressible Navier–Stokes equations in an exterior domain
in two dimensions. For numerical purposes we truncate the domain to a finite sub-domain, which leads to the problem of finding
so called “artificial boundary conditions” to replace the boundary conditions at infinity. To solve this problem we construct
– by combining results from dynamical systems theory with matched asymptotic expansion techniques based on the old ideas of
Goldstein and Van Dyke – a smooth divergence free vector field depending explicitly on drag and lift and describing the solution
to second and dominant third order, asymptotically at large distances from the body. The resulting expression appears to be
new, even on a formal level. This improves the method introduced by the authors in a previous paper and generalizes it to
non-symmetric flows. The numerical scheme determines the boundary conditions and the forces on the body in a self-consistent
way as an integral part of the solution process. When compared with our previous paper where first order asymptotic expressions
were used on the boundary, the inclusion of second and third order asymptotic terms further reduces the computational cost
for determining lift and drag to a given precision by typically another order of magnitude.
Peter Wittwer: Supported in part by the Fonds National Suisse. 相似文献
15.
IntroductionForlinearviscoelasticsystemsunderbothadditiveandmultiplicativebroad_bandexcitationexcitations,Ariaratnam[1]studiedthestochasticstabilityofthesystembyusingthemethodofstochasticaveragingprocedure .Itwasshownthatthevisco_elasticforcecontributedtowarddamping ,hence ,stabilityofthesystem .However,thestiffnesseffectofthevisco_elasticcomponentwasnotfullyaccountedfor.FurthermoreAriaratnam[2 ]studiedthestochasticstabilityofthesystembutthemodelislinear.Inthetheoryofnonlinearrandomvibration… 相似文献
16.
A solution is presented to verify numerical computer codes of reactive transport with both equilibrium and kinetic reactions.
A synthetic model of A ↔ B ↔ C → chain reactions is proposed to describe operator-splitting numerical schemes used in numerical
computer codes. A reaction matrix is derived for both the equilibrium and the first-order kinetic reactions and further decoupled
as a diagonal matrix. Therefore, the partial differential equations (PDEs) coupled by the reaction matrix can be transformed
into independent PDEs, for which closed-form solutions exist or can be derived. The solution derived in this study is compared
with numerical results. 相似文献
17.
To investigate the principal resonance in transverse nonlinear parametric vibration of an axially accelerating viscoelastic string, the method of multiple scales is applied directly to the nonlinear partial differential equation that governs the transverse vibration of the string. To derive the governing equation, Newton‘s second law, Lagrangean strain, and Kelvin‘s model are respectively used to account the dynamical relation, geometric nonlinearity and the viscoelasticity of the string material. Based on the solvability condition of eliminating the secular terms, closed form solutions are obtained for the amplitude and the existence conditions of nontrivial steady-state response of the principal parametric resonance. The Lyapunov linearized stability theory is employed to analyze the stability of the trivial and nontrivial solutions in the principal parametric resonance. Some numerical examples are presented to show the effects of the mean transport speed, the amplitude and the frequency of speed variation. 相似文献
18.
The principal resonance of a 3-DOF nonlinear system to narrow-band random external excitations is investigated. The method of multiple scales is used to derive the equations for modulation of amplitude and phase. The behavior, stability and bifurcation of steady-state responses are studied by means of qualitative analysis. The effects of damping, detuning, and excitation intensity on responses are analyzed. The theoretical analyses are verified by numerical results. Both theoretical analyses and numerical simulations show that when the intensity of the random excitation increases, the nontrivial steady state solution may change from a limit cycle to a diffused limit cycle. Under some conditions, co-existence of two kinds of stable steady-state solutions, saturation and jump phenomena may occur. The stationary probability density function of responses for the co-existence case is obtained approximately. 相似文献
19.
In this paper, a biochemical model with the impulsive perturbations is considered. By using the Floquet theorem for the impulsive
equation and small-amplitude perturbation skills, we see that the boundary-periodic solution ([(x)\tilde](t),0)(\tilde{x}(t),0) is locally stable if some conditions are satisfied. In a certain limiting case, it is shown that a nontrivial periodic solution
emerges via a supercritical bifurcation. By numerical simulation, we can show that the system presents rich dynamics, including
periodic solutions, quasi-periodic oscillations, period doubling cascades, periodic halving cascades, symmetry bifurcations,
and chaos. 相似文献
20.
Sebastian Bönisch Vincent Heuveline Peter Wittwer 《Journal of Mathematical Fluid Mechanics》2005,7(1):85-107
We consider the problem of solving numerically the stationary incompressible Navier–Stokes equations in an exterior domain in two dimensions. This corresponds to studying the stationary fluid flow past a body. The necessity to truncate for numerical purposes the infinite exterior domain to a finite domain leads to the problem of finding appropriate boundary conditions on the surface of the truncated domain. We solve this problem by providing a vector field describing the leading asymptotic behavior of the solution. This vector field is given in the form of an explicit expression depending on a real parameter. We show that this parameter can be determined from the total drag exerted on the body. Using this fact we set up a self-consistent numerical scheme that determines the parameter, and hence the boundary conditions and the drag, as part of the solution process. We compare the values of the drag obtained with our adaptive scheme with the results from using traditional constant boundary conditions. Computational times are typically reduced by several orders of magnitude. 相似文献