具有时滞和间接控制的捕食-被捕食模型的分支分析

研究了一类具有时滞和间接控制的捕食-被捕食模型.选择时滞τ为分支参数,证实了系统在一定的时滞范围内是渐近稳定的.当时滞τ通过一系列的临界值时,Hopf分支产生,即当时滞τ通过某些临界值时,从平衡点处产生一簇周期解.最后,用数值模拟验证了理论分析结果的正确性.     

Stabilization of oscillations in a phase transition model

In this paper, we analyze a model presenting formation of microstructure depending on the parameters and the initial data. In particular, we investigate how the presence of stochastic perturbations affects this phenomenon in its asymptotic behavior. Two different sufficient conditions are provided in order to prevent the formation of microstructure: the first one for Stratonovich noise while the second for Itô noise. The main contribution of the paper is that these conditions are independent of the initial values unlike in the deterministic model. Thus, we can interpret our results as some kind of stabilization produced by both types of noise. Copyright © 2016 John Wiley & Sons, Ltd.     

The economic production and pricing model with lot-size-dependent production cost

In this paper, the economic production quantity problem for a single-product single-machine system is extended. It is assumed that annual demand of the product is a function of price set by manufacturer. This extension considers sales revenue, inventory and setup costs as well as a variable cost of production which is a function of the lot size. Several linear and non-linear functions of demand and variable cost are considered in this paper and a global solution methodology is presented for the models developed. Newton??s method is used to find local optima and asymptotic convergence of the solution algorithm to a global optimum is proved. Numerical studies followed by a discussion provide additional insights into the problem.     

Magnetic catalysis in a P-even, chiral-invariant three-dimensional model with four-fermion interaction

We study how an external magnetic field H affects the phase structure of a P-even, chiral-invariant three-dimensional model of field theory with a four-fermion interaction. An arbitrarily small, but nonzero, magnetic field induces the spontaneous breaking of the initial symmetry (the magnetic catalysis phenomenon). Depending on the values of the coupling constants, the model vacuum is either P-even or chiral invariant for H≠0. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 124, No. 2, pp. 323–338, August, 2000.     

Impedance of a three-dimensional head-spine model

A three-dimensional, discrete mathematical model of the human spine, torso, and head is decribed. The model consists of a system of rigid bodies representing the head, vertebrae, pelvis, and viscera, interconnected by deformable elements representing the intervertebral discs, ligaments, and other connective tissues. The model is a modified version of a previously developed head-spine model, the primary modifications being the incorporation of a detailed representation of the viscera-abdominal wall system and the determining of more accurate model damping parameters. Driving point impedances for vertical (+G_z) excitation were numerically determined for both the modified and the older model and compared to experimentally obtained driving point impedances of human volunteers. It is shown that the modified model's impedance is in much better agreement with the experimental results than that of the older model.     

Stabilization in elastic solids with voids

In this paper we study the asymptotic behavior and the analyticity of the solutions of the one-dimensional porous-elasticity problem with thermal effect. Our main result is to prove the lack of exponential stability in case of the porous-elasticity with thermal effect when viscoelasticity is present. We prove the analyticity of the problem when a porous viscosity is present. We conclude by showing the impossibility of localization in time of the solutions in the isothermal case.     

Stabilization of traffic flow in optimal velocity model via delayed-feedback control

Traffic jams may occur due to various reasons, such as traffic accidents, lane reductions and on-ramps. In order to suppress the traffic congestion in an optimal velocity traffic model without any driver’s delay taken into account, a delayed-feedback control of both displacement and velocity differences is proposed in this study. By using the delay-independent stability criteria and the H_∞-norm, the delayed-feedback control can be determined to stabilize the unstable traffic flow and suppress the traffic jam. The numerical case studies are given to demonstrate and verify the new control method. Furthermore, a comparison is made between the new control method and the method proposed by Konishi et al. [K. Konishi, M. Hirai, H. Kokame, Decentralized delayed-feedback control of an optimal velocity traffic model, Eur. Phys. J. B 15 (2000) 715–722]. The results show that the new control method makes the traffic flow more stable and improves the control performance.     

An EPQ model with inflation in an imperfect production system

In this paper, a production inventory model is considered for stochastic demand with the effect of inflation. Generally, every manufacturing system wants to produce perfect quality items. However, due to real-life problems (labor problems, machine breakdown, etc.), a certain percentage of products are of imperfect quality. The imperfect items are reworked at a cost. The lifetime of a defective item follows a Weibull distribution. Due to the production of imperfect quality items, a product shortage occurs. The profit function is derived by using both a general distribution of demand and the uniform rectangular distribution of demand. Computational experiments along with graphical illustrations are presented to discuss the optimality of the probability functions.     

An inventory model with reliability in an imperfect production process

The paper analyzes an economic manufacturing quantity (EMQ) model with price and advertising demand pattern in an imperfect production process under the effect of inflation. If the machine goes through a long-run process, it may shift from in-control state to out-of-control state. As a result, the system produces imperfect items. The imperfect items are reworked at a cost to make it as new. The production of imperfect quality items increases with time. To reduce the production of the imperfect items, the systems have to more reliable and the produced items depend on the reliability of the machinery system. In this direction, the author considers that the development cost, production cost, material cost are dependent on reliability parameter. Considering reliability as a decision variable, the author constructs an integrated profit function which is maximized by control theory. A numerical example along with graphical representation and sensitivity analysis are provided to illustrate the model.     

Steady-state solutions in a three-dimensional nonlinear pool-boiling heat-transfer model

We consider a relatively simple model for pool-boiling processes. This model involves only the temperature distribution within the heater and describes the heat exchange with the boiling medium via a nonlinear boundary condition imposed on the fluid-heater interface. This results in a standard heat-transfer problem with a nonlinear Neumann boundary condition on part of the boundary. In a recent paper [Speetjens M, Reusken A, Marquardt W. Steady-state solutions in a nonlinear pool-boiling model. IGPM report 256, RWTH Aachen. Commun Nonlinear Sci Numer Simul, in press, doi:10.1016/j.cnsns.2006.11.002] we analysed this nonlinear heat-transfer problem for the case of two space dimensions and in particular studied the qualitative structure of steady-state solutions. The study revealed that, depending on system parameters, the model allows both multiple homogeneous and multiple heterogeneous temperature distributions on the fluid-heater interface. In the present paper we show that the analysis from Speetjens et al. (doi:10.1016/j.cnsns.2006.11.002) can be generalised to the physically more realistic case of three space dimensions. A fundamental shift-invariance property is derived that implies multiplicity of heterogeneous solutions. We present a numerical bifurcation analysis that demonstrates the multiple solution structure in this mathematical model by way of a representative case study.     

Dynamics of three-dimensional magnetic structures in the Heisenberg model

Theoretical and Mathematical Physics - We study the integrability of the dynamical Heisenberg equations (the $$O(3)$$ model in four-dimensional pseudo-Euclidean space–time), which are widely...     

Secondary bifurcations and localisation in a three-dimensional buckling model

This paper revisits the effect of secondary bifurcations on the post-buckling response of a simple 3D system of elastically restrained beams, first discussed by Luongo in [19]. Our main objective is to show how to construct a uniform asymptotic expression for the localised buckling patterns experienced by this model. The governing equation is formulated as a fourth-order eigenvalue problem with non-constant coefficients and then a complex WKB technique is employed to yield the localised instability patterns. Numerical simulations supporting the analytical findings are included as well.Received: October 21, 2003     

Secondary bifurcations and localisation in a three-dimensional buckling model

This paper revisits the effect of secondary bifurcations on the post-buckling response of a simple 3D system of elastically restrained beams, first discussed by Luongo in [19]. Our main objective is to show how to construct a uniform asymptotic expression for the localised buckling patterns experienced by this model. The governing equation is formulated as a fourth-order eigenvalue problem with non-constant coefficients and then a complex WKB technique is employed to yield the localised instability patterns. Numerical simulations supporting the analytical findings are included as well.     

Use of three-dimensional model of filler in stability problems for triple-layer shells with delaminations

Mechanics of Composite Materials -