Dynamical analysis of a nonlinear competitive model with generic and brand advertising efforts

In this paper, a new four-dimensional map is proposed to model the dynamical advertising efforts, where both the generic and brand effects for advertisement are taken into account in the model. The marginal profit adapting strategy is used to reflect the interaction among the firms that strive for the optimal profit. When the generic advertising bears a large effectiveness coefficient, the generic advertising efforts will exhibit chaos, which leads to a chaotic dynamics for brand advertising efforts. In this case, we analyze the some properties of steady trajectories that imply rough profiles of the advertising strategies evolution. Furthermore, by rigorous dynamical analysis and numerical simulations, we obtain the feasible set outlining the influence of initial conditions on the global dynamic properties. We first deal with the symmetric system, and then extend the obtained results to more general case, namely, the asymmetric model. For the symmetric model, two firms’ brand advertising expenditures behave synchronization, but the dynamics of generic advertising efforts are dependent upon initial conditions. Meanwhile, for the heterogeneous case, the domain firm in the market needs to contribute all generic advertising expenditures. Our results can have a practical impact on the market evolution, and are therefore beneficial to decision maker.     

A prognosis model for wear prediction based on oil-based monitoring

This paper reports on the development of a wear prediction model based on stochastic filtering and hidden Markov theory. It is assumed that observations at discrete time points are available such as metal concentrations from oil-based monitoring, which are related to the true underlying state of the system which is unobservable. The system state is represented by a generic term of wear which is modelled by a continuous hidden Markov Chain using a Beta distribution. We formulated a recursive model to predict the current and future system state given past observed monitoring information to date. The model is useful to wear-based monitoring such as oil analysis. Numerical examples are presented in the paper based on simulated and real data.     

Modelling the sustainability of mass tourism in island tourist economies

Tourism is one of the world's largest industries and is a source of jobs across national and regional economies. Assessing the economic, environmental and social impacts of tourism development has become a major activity within the tourism and sustainable development communities. The purpose of this research is to demonstrate the contribution of system dynamics for analysing policies that can not only promote sustainable tourism development, but also act as a warning signal to the industry about the potential negative consequences of uncontrolled growth of mass tourism, particularly in island tourist economies. Previous research in the tourism sector has been fragmented, when a holistic approach is needed in order to try to coerce some alignment in the views of the various stakeholders. The main research results illustrated in this paper are: a generic model of a tourism system informed by the (mainly) South European island tourist economies and a set of scenarios illustrating examples of policy analysis. The generic model and the modelling process developed in this research will have some transferability to other issues concerned with policymaking for sustainable development.     

MIMO capacity for deterministic channel models: sublinear growth

This is the second paper by the authors in a series concerned with the development of a deterministic model for the transfer matrix of a MIMO system. In our previous paper, we started from the Maxwell equations and described the generic structure of such a deterministic transfer matrix. In the current paper, we apply those results in order to study the (Shannon‐Foschini) capacity behavior of a MIMO system as a function of the deterministic spread function of the environment and the number of transmitting and receiving antennas. The antennas are assumed to fill in a given fixed volume. Under some generic assumptions, we prove that the capacity grows much more slowly than linearly with the number of antennas. These results reinforce previous heuristic results obtained from statistical models of the transfer matrix, which also predict a sublinear behavior. Copyright © 2012 John Wiley & Sons, Ltd.     

Can we have confidence in generic structures?

The system dynamics concept of ‘generic structure’ is dividable into three sub-types. This paper analyses the validity of these three, using both practical and theoretical perspectives. Firstly, a new set of measures is developed for generating validity—‘confidence’—amongst a group using generic structures in a practical modelling situation. It is concluded that different confidence criteria are implicitly employed; there is an argument for trading-off model precision and analytical quality for simplicity and ease of use and future research is needed to combine these ‘process’ and ‘content’ aspects of confidence. From a theoretical stance it is shown that with two of the sub-types a scientific notion of confidence is achievable whereas the third (‘archetypes’) involves merely metaphorical thinking. It is concluded that the theoretical status of archetypes requires further development, whilst ensuring that its benefits are retained.     

Generic cuts in models of arithmetic

We present some general results concerning the topological space of cuts of a countable model of arithmetic given by a particular indicator Y. The notion of “indicator” is de.ned in a novel way, without initially specifying what property is indicated and is used to de.ne a topological space of cuts of the model. Various familiar properties of cuts (strength, regularity, saturation, coding properties) are investigated in this sense, and several results are given stating whether or not the set of cuts having the property is comeagre. A new notion of “generic cut” is introduced and investigated and it is shown in the case of countable arithmetically saturated models M ? PA that generic cuts exist, indeed the set of generic cuts is comeagre in the sense of Baire, and furthermore that two generic cuts within the same “small interval” of the model are conjugate by an automorphism of the model.The paper concludes by outlining some applications to constructions of cuts satisfying properties incompatible with genericity, and discussing in model‐theoretic terms those properties for which there is an indicator Y. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Syntactic approach to constructions of generic models

A syntactic approach is described to constructing generic models which generalizes the known semantic one. A sufficient condition of a generic model being homogeneous is specified. It is shown that, within the syntactic approach, any countable homogeneous model is generic. Criteria and a sufficient condition are given for the generic models created in syntactic constructions to be saturated. Supported by RFBR grant No. 05-01-00411, and by the Council for Grants (under RF President) and State Aid of Fundamental Science Schools via project NSh-4787.2006.1. __________ Translated from Algebra i Logika, Vol. 46, No. 2, pp. 244–268, March–April, 2007.     

Reconnection in a global model of Poincaré map describing dynamics of magnetic field lines in a reversed shear tokamak

Magnetic field lines behaviour in a reversed shear tokamak can be described by a one and a half degree of freedom Hamiltonian system. In order to get insights into its dynamics we study numerically a global model for a Poincaré map associated to such a system. Mainly we investigate the scenario of reconnection of the invariant manifolds of two hyperbolic orbits of the same type n/m and show that it is a generic one. When the two Poincaré–Birkhoff chains involved in this process are aligned in phase, i.e. they are in a nongeneric position, a sequence of two saddle–center bifurcations occur in one of the chains, interfering with the former elliptic orbit of that chain, such that at the reconnection threshold the two chains are in a generic position. Dynamics around the new created configuration at the reconnection appears to vary from a regular motion to a chaotic one.

In connection with the study of this global bifurcation we give the first example of region of instability in the dynamics of a nontwist map.     

On the Weak Kowalevski–Painlevé Property for Hyperelliptically Separable Systems

We consider so called hyperelliptically separable systems (h.s.s.) arising in various physical problems, whose generic invariant manifolds can be completed either to hyperelliptic Jacobians or to their nonlinear subvarieties (strata) or their finite coverings. In the case of strata the algebraic geometrical structure of such systems has much in common with that of algebraic completely integrable systems (a.c.i.s.). Using this property we study formal singular solutions of a.c.i.s. and h.s.s., which may contain fractional powers of time. We give estimates for the number and leading behavior of their principal and lower balances both for a generic and for the so called physical direction of the flow. This can be regarded as an useful extension of the Kowalevski–Painlevé integrability test. We also prove that when the system is h.s. but not a.c.i., its generic solutions are single-valued on an infinitely sheeted ramified covering of the complex time plane. Some model examples are considered, such as the hierarchy of integrable generalizations of the Henon–Heiles and the Neumann systems.     

A generic model for spouse’s pensions with a view towards the calculation of liabilities

We introduce a generic model for spouse’s pensions. The generic model allows for the modeling of various types of spouse’s pensions with payments commencing at the death of the insured. We derive abstract formulas for cashflows and liabilities corresponding to common types of spouse’s pensions. In particular, we show that our generic model allows for simple modeling of longevity improvements, enabling the calculation of the Solvency II capital requirements related to longevity risk for spouse’s pensions.     

不确定条件下n人非合作博弈均衡点集的通有稳定性

基于经典博弈模型的Nash均衡点集的通有稳定性和具有不确定参数的n人非合作博弈均衡点的概念,探讨了具有不确定参数博弈的均衡点集的通有稳定性.参照Nash均衡点集稳定性的统一模式,构造了不确定博弈的问题空间和解空间,并证明了问题空间是一个完备度量空间,解映射是上半连续的,且解集是紧集（即usco（upper semicontinuous and compact-valued）映射）,得到不确定参数博弈模型的解集通有稳定性的相关结论.     

The differential quadrature element method irregular element torsion analysis model

The differential quadrature element method (DQEM) has been proposed. The element weighting coefficient matrices are generated by the differential quadrature (DQ) or generic differential quadrature (GDQ). By using the DQ or GDQ technique and the mapping procedure the governing differential or partial differential equations, the transition conditions of two adjacent elements and the boundary conditions can be discretized. A global algebraic equation system can be obtained by assembling all of the discretized equations. This method can convert a generic engineering or scientific problem having an arbitrary domain configuration into a computer algorithm. The DQEM irregular element torsion analysis model is developed.     

Resolution of a scheduling problem in a flowshop robotic cell

We develop in this paper a generic and precise identification of a scheduling problem in a flexible manufacturing system. We consider a flowshop robotic cell that processes several jobs. We assume that there is no intermediate buffer between machines. So, jobs may be blocked when downstream machines are busy. We present an integer programming model to determine the sequence of jobs that minimizes the makespan criterion. In order to solve large size problems, we propose a genetic algorithm (GA). Finally, computational experiments are proposed in order to compare the makespan returned by the GA to a lower bound.     

Hopf bifurcation and the centers on center manifold for a class of three-dimensional Circuit system

In this paper, Hopf bifurcation and center problem for a generic three-dimensional Chua's circuit system are studied. Applying the formal series method of computing singular point quantities to investigate the two cases of the generic circuit system, we find necessary conditions for the existence of centers on a local center manifold for the systems, then Darboux method is applied to show the sufficiency. Further, we determine the maximum number of limit cycles that can bifurcate from the corresponding equilibrium via Hopf bifurcation.     

Scheduling at coal handling facilities using Simulated Annealing

The main thrust of this study is the operational scheduling of the continuous coal handling and blending processes when considering multiple, and sometimes conflicting, objectives. A widely applicable generic goal programming model is proposed. Furthermore, assumptions regarding the certainty of demand during different periods are challenged, endeavoring to provide more robust schedules in a largely stochastic environment. As the study aims to provide scheduling solutions to any coal handling facility, the Simulated Annealing metaheuristic is proposed to ensure that acceptably good solutions for large instances of the generic model can be found in reasonable computational time. The generic approach and its suggested application will be valuable not only in the coal handling environment, but also in the continuous product manufacturing/blending or continuous material handling environment.     

Event detection occurrence for planar piece-wise affine hybrid systems

Many switched circuits are made of linear components switched by a simple logic unit. In this paper, we use a generic planar Piece-wise Affine Hybrid System (PWAHS) to model this kind of circuit. Usually, simulations are run by analytical methods (adapted to a specific simple model) or by numerical simulations that can miss some events’ occurrences. We propose a generic planar method to simulate PWAHSs with periodic and state dependent events. Using analytical expressions, our approach can reach arbitrary accuracy in event detections without any loss. As a result, we have implemented our method in Scilab and Matlab toolboxes.     

Novel global stability criteria for high-order Hopfield-type neural networks with time-varying delays

This paper discusses a generalized model of high-order Hopfield-type neural networks with time-varying delays. Some novel global stability criteria of the system is derived by using Lyapunov method, linear matrix inequality (LMI) and analytic technique. The LMI-based criteria obtained here are computationally more flexible and more generic than many other existing criteria. A numerical example is given to illustrate our result.     

A generic mathematical model of single point cutting tools in terms of grinding parameters

The paper presents the analytical geometric details of the mathematical modeling of a single point cutting tool with a generic profile. The grinding angles and the ground depths on the tool are allowed to vary along the tool flanks and face, altering the cutting angles from point to point. The surface modeling begins with the creation of a tool blank model. Then unbounded surfaces are considered and transformed to get the cutting tool surfaces. The intersection of these surfaces gives the complete model of the tool. Starting from the basic model where the tool face and flank are planar, the generalization of the geometric design has been done in two steps to give free-form shapes to the tool surfaces, termed as the two generations of the generic profile. Then a forward and inverse mapping has been presented for the basic model and the two generations of the generic tool to relate the grinding angles with the prevalent nomenclatures (ASA, ORS and NRS). The model has been validated and the variation of tool angles with the grinding parameters has been illustrated with an example.     

Existence of diffusion orbits in a lattice system

We study a model which is a periodic lattice system with nearest neighbors coupling. Using the variational methods, we show the existence of diffusion orbits under a generic perturbation of time periodic.