The interaction of elements in a financial system can exhibit complex dynamic behaviours. In this article, we use a system of differential equations to model the evolution of a financial system and study its complexity. Numerical simulations show that the system exhibits a variety of rich dynamic behaviours, including chaos. Bifurcation diagrams show that the system behaves chaotically over a wide range of system parameters.

We investigate game-theory based decisions on vaccination uptake and its effects on the spread of an epidemic with nonlinear incidence rate. It is assumed that each individual’s decision approximates his/her best response (called smoothed best response) in that this person chooses to take the vaccine based on its cost-benefit analysis. The basic reproduction number of the resultant epidemic model is calculated and used to characterize the existence and stability of the disease-free and endemic equilibria of the model. The effects on the spread and control of the epidemic are revealed in terms of the sensitivity of the response to changes in costs and benefits, in the “cost” of the vaccination, and in the proportion of susceptible individuals who are faced with the decision of whether or not to be vaccinated per unit time. The effects of the best response decision rule are also analyzed and compared to those of the smoothed best response. Our study shows that, when there is a perceived cost to take the vaccine, the smoothed best response is more effective in controlling the epidemic. However, when this cost is 0, the best response is the more efficient control.

It is of great significance to deal with the relationship between external factors and the water-energy-food internal system for China’s sustainable development. This paper takes China as the research object, uses the system dynamics method to construct a model for China’s water-energy-food system, and introduces the “two-child” policy and trade friction as the scenario parameters for simulation. The main results of scenario simulation can be summarized as the following three points. In terms of water, the trade friction will hinder China’s industrial water consumption into a low-consumption stage. In terms of energy, both the trade friction and the “two-child” policy, will not change the increasing trend of energy demand. In terms of food, if there is strong response to the “two-child” policy, there will be insufficient food inventory under the current capacity and import ratio. In short, this paper takes the sustainable development of water-energy-food as a starting point and puts forward policy suggestions on the comprehensive formulation of policies.