Search

Based on the deterministic network infectious disease model, a stochastic network infectious disease model under the influence of white noise was established, and the existence and uniqueness of the global solution to the model were proved. With the theory of stochastic differential equations, sufficient conditions for stochastic extinction and persistence of infectious diseases were obtained. The results show that, white noise has a great impact on the transmission dynamics of network infectious diseases. White noise can effectively suppress the spread of infectious diseases, and large white noise can even make the original persistent infectious diseases become extinct. Finally, the theoretical results were verified through numerical simulations. [ABSTRACT FROM AUTHOR]

The dynamic behavior of a stochastic predator-prey model with the Gilpin-Ayala growth was studied. The existence and uniqueness of the global positive solution to the system were proved, and sufficient conditions for system extinction and persistence were obtained. On this basis, the thresholds for controlling the stochastic persistence and extinction of the predator-prey system were given, and some asymptotic behaviors of the solution were discussed. Finally, the effectiveness of the results was verified through numerical simulation. [ABSTRACT FROM AUTHOR]

To rationally allocate air traffic rights（ATR）and avoid vicious competition of airlines for scarce passenger air traffic right resources，the air traffic right allocation problem（ATRAP）is proposed originally， and a mixed integer programming （MIP） model for this problem was established. The model aims at reasonably allocating scarce ATR resources to domestic airlines and international airports. With the known origin-destination（OD）distribution of passengers of two countries，the objective of this model is to minimize the travel mileage of passengers，and comprehensively considers the level of international hub airport，the competitiveness level of airlines and market share. Constraints include air traffic right resources，airline operating capacity，flight load，etc. Then a genetic algorithm is designed to solve the problem，and the optimization solver named CPLEX as well as the genetic algorithm is used to carry out calculation example experiments to verify the correctness of the model and the effectiveness of the algorithm. Finally，the practical application of the allocation of ATR between China and France is carried out. [ABSTRACT FROM AUTHOR]

A modified Euler-Maruyama ( EM) scheme was constructed for a class of multi-term fractional non-linear stochastic differential equations with weak singularity kernels, and the strong convergence of this modified EM scheme was proved. Specifically, according to the sufficient condition for stochastic integral decomposition, the multi-term fractional stochastic differential equation was equivalently transformed into the stochastic Volterra integral equation, and then the corresponding modified EM scheme and its strong convergence were derived and proved, respectively. The order of strong convergence is an, - αm - αm-1 where αi is the index of fractional derivative satisfying 0 < α1, < ... < αm-1 <α1 <1. Finally, numerical experiments verify the correctness of the theoretical results. [ABSTRACT FROM AUTHOR]

The research on population dynamics and related control problems is not only of theoretical significance, but also closely related to biodiversity protection, pest control, and the development and utilization of renewable resources. The optimal harvesting problem was considered in a periodic 3-species predator-prey system with 1 predator and 2 competing preys, where the predator has size structure and was described with 1st-order partial differential equations. First, the existence of a unique non-negative solution of the controlled system was proven by means of the fixed-point reasoning, and the continuous dependence of the solution on the control variables was discussed. Then, the optimal harvesting conditions were given with the techniques of tangential-normal cones and the adjoint system. Finally, with Ekeland's variational principle, the existence of the optimal harvesting strategy was derived. Here the objective functional represents the net economic benefit in the harvesting of 3 species. The results obtained would be beneficial for exploration of renewable resources. [ABSTRACT FROM AUTHOR]

Integrated defense against earthquake disaster is an urgent problem. In this paper, the basic principle of urban multi-lines for seismic defense was proposed. The basic theory of defense periphery for urban earthquake disaster was established. The exchange rate between periphery groups was regard as control variable, and the Lotka-Volterra model was introduced into defense periphery system. The evolution model of urban multi-lines for earthquake disaster defense was set up, which explained the competition and collaboration dynamic mechanism of urban multi-lines for seismic defense. The order parameters of multi-lines defense system were selected according to synergy principle. The co-evolution measurement model of urban multi-lines for defensing earthquake was established, and it was applied to Nantong city earthquake disaster integrated defense system. The result shows that competition alienation characteristics of defense system arise, and system coordination degree is reduced to 0.62. The system is restored to the previous level of coordination degree, and it is developing towards coordinated direction by adjusting the input proportion of multi-lines for seismic defense. [ABSTRACT FROM AUTHOR]

The loss of social-pattern crisis will be extremely increased because of the distortion of crisis information in the diffusion process. Study on the diffusion rule of crisis information will contribute to active response to social-pattern crisis. There are two types of crisis information: true information and false information. The diffusion process of social-pattern crisis information is viewed as the dynamic competitive process of crisis information diffusion between true information and false information which strives for trust of victims based on ecology. This paper posits a social-pattern crisis information diffusion model based on Lotka-Volterra model. Then it conducts simulation and empirical study utilizing this model. The results show that the equilibrium state is only related with the substitute coefficient. The time achieving the balance is positively related with the difference of diffusivity; and the inflection point in the diffusion process of crisis information is decided by the substitute coefficient, diffusivity and initial state. We put forward some suggestions which establish the sharing system of crisis information, release system of crisis information and multiple-participation mechanism for crisis responses. [ABSTRACT FROM AUTHOR]