Control of chaotic systems through reservoir computing.

Chaos is an important dynamic feature, which generally occurs in deterministic and stochastic nonlinear systems and is an inherent characteristic that is ubiquitous. Many difficulties have been solved and new research perspectives have been provided in many fields. The control of chaos is another problem that has been studied. In recent years, a recurrent neural network has emerged, which is widely used to solve many problems in nonlinear dynamics and has fast and accurate computational speed. In this paper, we employ reservoir computing to control chaos in dynamic systems. The results show that the reservoir calculation algorithm with a control term can control the chaotic phenomenon in a dynamic system. Meanwhile, the method is applicable to dynamic systems with random noise. In addition, we investigate the problem of different values for neurons and leakage rates in the algorithm. The findings indicate that the performance of machine learning techniques can be improved by appropriately constructing neural networks.

Effect of the policy and consumption delay on the amplitude and length of business cycle.

In this paper, the amplitude and the length of the business cycle are investigated. It is the first time the length of the business cycle based on the Goodwin model (one classical business cycle model) is discussed. The effect of the time delay of the economic policy and consumption on the amplitude and the length of the business cycle is studied. Meanwhile, the memory property of making economic policy is also considered. The theoretical amplitude of the business cycle is obtained by multiple-scale methods. The transitions of the amplitude induced by memory property and time delay are analyzed. How the economic parameter and random excitation affect the length of the business cycle is proposed. Based on the results, we can find that the time delay of both economic policy and consumption can induce the transitions. Moreover, the memory property of economic policy will change the critical value of the parameters when the transitions occur. In one typical induced investment function, the length of the business cycle is determined only by the autonomous investment and consumption. However, the length of the business cycle is not mainly affected by the autonomous investment and consumption in some other typical induced investment function. This states that the type of induced investment function has a very important role in determining the length of the business cycle.