The asymptotic stability analysis in stochastic logistic model with Poisson growth coefficient

The asymptotic stability of a discrete logistic model with random growth coefficient is studied in this paper. Firstly, the discrete logistic model with random growth coefficient is built and reduced into its deterministic equivalent system by orthogonal polynomial approximation. Then, the linear stability theory and the Jury criterion of nonlinear deterministic discrete systems are applied to the equivalent one. At last, by mathematical analysis, we find that the parameter interval for asymptotic stability of nontrivial equilibrium in stochastic logistic system gets smaller as the random intensity or statistical parameters of random variable is increased and the random parameter’s influence on asymptotic stability in stochastic logistic system becomes prominent.

Stochastic bifurcation and density function analysis of a stochastic logistic equation with distributed delay and strong kernel

Since the stochastic bifurcation theory is still in its infancy,we try to analyze some stochastic bifurcation phenomenon from a simple mathematical model.Thus,this paper mainly focuses on studying the stochastic bifurcation of a stochastic logistic model with distributed delay in the strong kernel case,which is affected by noise.Therefore,we use the intrinsic growth rate as a bifurcation parameter.First,we study the stochastic D-bifurcation and stochastic P-bifurcation for stochastic logistic model.Furthermore,by deriving the corresponding Fokker-Planck equation,we obtain the expression of the joint density function of the stochastic logistic system near the positive equilibrium point.Finally,some conclusions are given.

Effect of time-of-day and day-of-the-week on congestion duration and breakdown:A case study at a bottleneck in Salem,NH

This work uses regression models to analyze two characteristics of recurrent congestion： breakdown, the transition from freely flowing conditions to a congested state, and duration, the time between the onset and clearance of recurrent congestion. First, we apply a binary logistic regression model where a continuous measurement for traffic flow and a dichoto- mous categorical variable for time-of-day （AM- or PM-rush hours） is used to predict the probability of breakdown. Second, we apply an ordinary least squares regression model where categorical variables for time-of-day （AM- or PM-rush hours） and day-of-the-week （Monday-Thursday or Friday） are used to predict recurrent congestion duration. Models are fitted to data collected from a bottleneck on 1-93 in Salem, NH, over a period of 9 months. Results from the breakdown model, predict probabilities of recurrent congestion, are consistent with observed traffic and illustrate an upshift in breakdown probabilities between the AM- and PM-rush periods. Results from the regression model for congestion duration reveal the presences of significant interaction between time-of-day and day-of-the-week. Thus, the effect of time-of-day on congestion duration depends on the day-of-the-week. This work provides a simplification of recurrent congestion and recovery, very noisy processes. Simplification, conveying complex relationships with simple statistical summaries-facts, is a practical and powerful tool for traffic administrators to use in the decision-making process.