Noise processes in large ring lasers

Large ring lasers with a cavity Q well above 10¹² are characterized by extremely narrow line-widths and high coherence. At this point, active Sagnac interferometers do not quite reach the quantum limit. In this paper, we will explore the current status of this technology and look at the various noise processes involved with large ring lasers rigidly mounted to the Earth crust.     

GLOBAL ATTRACTIVITY IN A PERIODIC COMPETITION SYSTEM WITH FEEDBACK CONTROLS

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Single facility location on a network under mill and delivered pricing

^** E-mail: pelegrin{at}um.es Firms normally use either a mill price or a delivered pricepolicy, depending on market conditions (type of good, transportationway, customers location, costs, etc). In this paper, the problemof selecting the best location for an entering firm in competitionwith some pre-existing firms, under each price policy, is studiedon a network for the first time. With mill pricing, an equilibriumin price rarely exists and it is assumed that all competingfirms set a common mill price for all customers. With deliveredpricing, there exists a Nash equilibrium in price and it isassumed that the equilibrium price in each area is offered tothe customers in that area. In both cases, we consider thatcustomers buy from the cheapest facility and the same rulesare used for tie breaking in the lowest cost. While the profitmaximization problem for the entering firm always has optimalsolutions under mill pricing, this problem might not have anoptimal solution under delivered pricing. We show some discretizationresults and give procedures to find the full set of optimal,or -optimal, solutions to the problem under the two price policies.A comparison of results with the two price policies is givenby using an illustrative example.     

Some new results on the permanence and extinction of nonautonomous Gilpin–Ayala type competition model with delays

In this paper, we consider a delayed nonautonomous n-species Gilpin–Ayala type competitive system, which is more general and more realistic then classical Lotka–Volterra type competition model. For each rn, we establish a series of criteria under which r of the species in the system are permanent while the remaining n-r species are driven to extinction.     

A low-dimensional model of binocular rivalry using winnerless competition

We discuss a novel minimal model for binocular rivalry (and more generally perceptual dominance) effects. The model has only three state variables, but nonetheless exhibits a wide range of input and noise-dependent switching. The model has two reciprocally inhibiting input variables that represent perceptual processes active during the recognition of one of the two possible states and a third variable that represents the perceived output. Sensory inputs only affect the input variables.We observe, for rivalry-inducing inputs, the appearance of winnerless competition in the perceptual system. This gives rise to a behaviour that conforms to well-known principles describing binocular rivalry (the Levelt propositions, in particular proposition IV: monotonic response of residence time as a function of image contrast) down to very low levels of stimulus intensity.     

Analysis of dynamics in a general intraguild predation model with intraspecific competition

This paper is devoted to studying the dynamical properties of a general intraguild predation model with intraspecific competition. We first investigate the stability of all possible equilibria in relation to the ecological parameters, and then study the long time behavior of the solution. Moreover, we provide a detailed analysis of dynamics of a IGP model with linear functional response and intraspecific competition. Our results show that the impact of the intraspecific competition essentially increases the dynamical complexity of the system.     

Stability and Hopf bifurcation of a delayed predator-prey system with nonlocal competition and herd behaviour

In this paper, we investigate the stability and Hopf bifurcation of a diffusive predator-prey system with herd behaviour. The model is described by introducing both time delay and nonlocal prey intraspecific competition. Compared to the model without time delay, or without nonlocal competition, thanks to the together action of time delay and nonlocal competition, we prove that the first critical value of Hopf bifurcation may be homogenous or non-homogeneous. We also show that a double-Hopf bifurcation occurs at the intersection point of the homogenous and non-homogeneous Hopf bifurcation curves. Furthermore, by the computation of normal forms for the system near equilibria, we investigate the stability and direction of Hopf bifurcation. Numerical simulations also show that the spatially homogeneous and non-homogeneous periodic patters.     

Oligopoly newsvendor competition with reference effects

We analyze the equilibrium of a behavioral newsvendor game featuring oligopoly competition, where each newsvendor’s decision is driven by a reference effect regarding her potential profit. We find that the equilibrium order quantities are characterized by behavioral critical fractiles, where each newsvendor only accounts for the actions of competitors with smaller behavioral critical fractiles. Our result generalizes findings from recent literature on duopoly newsvendor competition with reference effects.     

Global dynamics of a population model from river ecology

In this paper, we investigate the population dynamics of a two-species Lotka-Volterra competition system arising in river ecology. An interesting feature of this modeling system lies in the boundary conditions at the downstream end, where the populations may be exposed to differing magnitudes of loss of individuals. By applying the theory of principal eigenvalue and monotone dynamical systems, we obtain a complete understanding on the global dynamics, which suggests that slower dispersal is selected for. Our results can be seen as a further development of a recent work by Tang and Chen (J. Differential Equations, 2020, 2020(269), 1465--1483).     

市场接纳不确定下短周期新产品产能投资研究 ——考虑竞争的投资时机与规模决策

新产品的市场接纳具有很大不确定性,传统投资理论并不适用于新产品投资。针对新产品投资中的产能投资,研究了垄断企业和有成本差异的竞争企业制定短周期新产品的产能投资时机与规模策略。给定企业“早”和“晚”两个投资时机可供选择,定义“早”投资时,企业只知道新产品市场规模的期望和方差;“晚”投资时,企业知道新产品真实的市场规模。垄断企业进入市场之前无法进行销售信息的收集,只会选择“早”投资或者不投资,给出其选择“早”投资的条件、最优产能投资规模及最大期望利润。有成本差异企业竞争的情形可以分为四种,分别给出四种情形下的最优产能投资规模及最大期望利润,并通过比较各情形下两企业的最大期望利润给出最优的产能投资时机策略。