Semistability of Nonlinear Systems Having a Continuum of Equilibria and Time-Varying Delays

Mitigation of tipping point transitions by time-delay feedback control

In stochastic multistable systems driven by the gradient of a potential, transitions between equilibria is possible because of noise. We study the ability of linear delay feedback control to mitigate these transitions, ensuring that the system stays near a desirable equilibrium. For small delays, we show that the control term has two effects: i) a stabilizing effect by deepening the potential well around the desirable equilibrium, and ii) a destabilizing effect by intensifying the noise by a factor of $(1-τα)^{-1/2}$, where $τ$ and $α$ denote the delay and the control gain, respectively. As a …

Pest control using farming awareness: impact of time delays and optimal use of biopesticides

We investigate a mathematical model in crop pest management, considering plant biomass, pest, and the effect of farming awareness. The pest population is divided into two compartments: susceptible pest and infected pest. We assume that the growth rate of self-aware people is proportional to the density of healthy pests present in the crop field. Impacts of awareness is modeled via a saturated term. It is further assumed that self-aware people will adopt biological control methods, namely integrated pest management. Susceptible pests are detrimental to crops and, moreover, there may be some tim…

异质通勤者走廊问题的排队替代原理

Queue replacement principle for corridor problems with heterogeneous commuters

本研究针对走廊网络中异质通勤者的出发时间选择问题，提出了一种解析方法来求解动态系统最优（DSO）和动态用户均衡（DUE）问题，并证明了排队替代原理（QRP）以推导闭式DUE解及多种政策下的均衡解。