Adaptive critic design and Hopfield neural network based simulation of time delayed photosynthetic production and prey–predator model

This paper presents a neural networks simulation of two complex adaptive ecological systems with a discrete time delay. The first system is related to the photosynthetic production of phytoplankton, the second with a time delayed prey–predator system incorporating a prey refuge. The iterative adaptive critic design is developed to simulate the maximal photosynthetic production of the mechanistic model of phytoplankton photosynthesis with discrete time delays. The prey–predator system is simulated using back-propagation learning of infinite-dimensional dynamical systems. The proposed simulation method is based on the time-dependent recurrent learning of continuous-time Hopfield neural network with a discrete time delay with the prey–predator system as a teacher signal. Furthermore, numerical calculations are included to demonstrate the proposed simulation algorithms.