Stability analysis of a cobweb model with market interactions

This paper explores the steady-state properties and the dynamic behavior of a generalization of the classical cobweb model. Under fairly general demand and cost functions, producers form naïve expectations about future prices and select their output so as to maximize expected profits. Unlike the traditional setup, producers have the choice between two markets, and tend to enter that which was more profitable in the recent past. Such a switching process implies time-varying aggregated supply schedules, thus representing a further source of nonlinearity for the dynamics of prices. Analytical investigations and the numerical simulation of a particular case with linear demand and supply indicate that such interactions may destabilize otherwise stable markets and generate complex dynamics.     

基于个体策略选择的知识传播研究

本文采用小世界网络模型模拟现实组织结构,构建了组织内部基于个体策略选择的知识传播模型,探讨了个体策略选择和网络结构对组织内部知识传播效果的影响。研究发现组织中无条件传播知识的个体的数量与平均知识水平成正比,对知识传播起促进作用;在网络结构方面,小世界网络对知识传播更加有利;组织规模较小时,更换策略的时间间隔对知识传播有较大影响。研究结果为组织有效地促进知识传播提供了支持。     

Surface‐enhanced Raman spectra of individual multiwalled carbon nanotubes with small innermost diameters

The Raman spectra of individual multiwalled carbon nanotubes (MWCNTs) with the innermost diameters of 0.6–0.9 nm are studied by surface‐enhanced Raman scattering. The influences of small innermost diameters to Raman features are investigated. A clear and relatively sharp Raman peak appears at 1510 cm⁻¹ when the innermost diameter is close to 0.6 nm. Lorentzian fits of G band indicate that its splitting is affected by the small innermost diameter of MWCNT. Moreover, the splitting of 2iTO mode is also observed at 2800–3000 cm⁻¹. Copyright © 2012 John Wiley & Sons, Ltd.     

Convergence of aspirations and (partial) cooperation in the prisoner's dilemma

This paper proposes an aspiration-based dynamic model for cooperation where a large population of agents are matched afresh every period to play a Prisoner's Dilemma. At each point in time, agents hold a common aspiration level which is updated on the basis of some “population statistic”, i.e. a certain scalar summary (e.g. average payoff) associated to the current state. On the other hand, those agents who feel “dissatisfied” (relative to current aspiration) switch actions at a rate which is increasing in the magnitude of the dissatisfaction. The resulting process is shown to converge in the long run under quite general conditions. Moreover, if agents are responsive enough, the long-run social state displays some extent of cooperation, with a constant positive fraction of the population (always less than half) choosing to cooperate in every period. Received: January 1998/Revised version: October 1998     

Partial differential integral equation model for pricing American option under multi state regime switching with jumps

In this paper, we consider a two dimensional partial differential integral equation (PDIE) model for pricing American option. A nonlinear rationality parameter function for two asset problems is introduced to deal with the free boundary. The rationality parameter function is added in the PDIEs used for pricing American option problems under multi-state regime switching with jumps. The resulting two dimensional nonlinear system of PDIE is then numerically solved. Based on real poles rational approximation, a strongly stable highly efficient and reliable method is developed to solve such complicated systems of PIDEs. The method is build in a predictor corrector style which makes it linearly implicit, therefore, avoids solving nonlinear systems of equations at each time step in all regimes. The method is seen to maintain the stability and convergence for large jump sizes and high volatility in each regime. The impact of regime switching on option prices corresponding to different values interest rate, volatility, and rationality parameter is computed, illustrated by graphs and given in the tables. Convergence results in each regime are presented and time evolution graphs are given to show the effectiveness and reliability of the method.     

Dynamics of a Deterministic and Stochastic Susceptible-exposed-infectious-recovered Epidemic Model

We investigate a susceptible-exposed-infectious-recovered (SEIR) epidemic model with asymptomatic infective individuals. First, we formulate a deterministic model, and give the basic reproduction number $\mathcal{R}_{0}$. We show that the disease is persistent, if $\mathcal{R}_{0}>1$, and it is extinct, if $\mathcal{R}_{0}<1$. Then, we formulate a stochastic version of the deterministic model. By constructing suitable stochastic Lyapunov functions, we establish sufficient criteria for the extinction and the existence of ergodic stationary distribution to the model. As a case, we study the COVID-19 transmission in Wuhan, China, and perform some sensitivity analysis. Our numerical simulations are carried out to illustrate the analytic results.