A discrete two-species competitive model is investigated. By using some preliminary lemmas and constructing a Lyapunov function, the existence and uniformly asymptotic stability of positive almost periodic solutions of the system are derived. In addition, an example and numerical simulations are presented to illustrate and substantiate the results of this paper.
A stage-structured prey-predator model with time delay and harvesting is considered. Some novel sufficient conditions for the local stability of the positive equilibria are obtained by Routh-Hurwitz criteria. Moreover, the existence of a Hopf bifurcation at the coexistence equilibrium is established. Finally, the optimal harvesting problem is formulated and solved by Pontryagin's maximum principle, and an example is given for illustration.
ARTICLE HISTORY
-The power of controlled generators in microgrids randomly fluctuate because of the stochastic volatility of the outputs of photovoltaic systems and wind turbines as well as the load demands. To address and dispatch these stochastic factors for daily operations, a dynamic economic dispatch model with the goal of minimizing the generation cost is established via chance-constrained programming. A Monte Carlo simulation combined with particle swarm optimization algorithm is employed to optimize the model. The simulation results show that both the objective function and constraint condition have been tightened and that the operation costs have increased. A higher stability of the system corresponds to the higher operation costs of controlled generators. These operation costs also increase along with the confidence levels for the objective function and constraints.
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