| In population ecosystems, the relations of the populations are described by dynamic models. On the basis of the analysis for the models, some complexity phenomena such as catastrophe are investigated and are shown by the nonlinear models, which has added the difficulties to analysis and control of the models. However, many nonlinear dynamic models can be represented by T-S fuzzy models, and the corresponding analysis and control are carried out by linear systems theory. On the other hand, the T-S fuzzy models with higher accuracy are proposed using the neural network. Thus, on the background of strawberry ecosystems, some population models are built up. Combine neural network with fuzzy system theory, corresponding T-S fuzzy models are obtained. The controllers are designed to stabilize the models at the ideal states, and simulations are carried out to prove the results. The specific contents are as follows:1. Based on Logistic model and the fuzziness of the Botrytis cinerea, a T-S fuzzy model is given using the sector nonlinearity. According to Lyapunov stability theorem, some sufficient conditions of the global stability of the model are given. And the controller is designed to keep the gray germs in the low population density.2. Based on the fold catastrophe model, a singular system model on strawberry population and aphid population is proposed. Graphic method is used to study the stability of the equilibria. Combine neural network with fuzzy system theory, the T-S fuzzy singular system model is obtained. According to the stability theory of the singular system, the sufficient conditions of the global stability of the equilibrium point are given. And the controller is designed to maintain the aphid population at the level which has done no harm to the strawberry population.3. Based on the catastrophe model, a singular system model on strawberry population, enemy population and aphid population is proposed. For the state of aphid population high density, the corresponding T-S fuzzy singular system model is given, and the controller is designed to make the model stable at the ideal state which the aphid population density is low and the strawberry population density is high. |
