Bifurcations and chaos control in discrete small-world networks

An impulsive delayed feedback control strategy to control period-doubling bifurcations and chaos is proposed. The control method is then applied to a discrete small-world network model. Qualitative analyses and simulations show that under a generic condition, the bifurcations and the chaos can be delayed or eliminated completely. In addition, the periodic orbits embedded in the chaotic attractor can be stabilized.

Exponential Estimation of the Lyapunov Function for Delay-Coupled Neural Networks with Integral Terms

This paper investigates a class of coupled neural networks with delays and ad-dresses the exponential synchronization problem using delay-compensatory impulsive control. Razumikhin-type inequalities involving some destabilizing delayed impulse gains are proposed, along with a new delay-compensatory concept demonstrating two crucial roles in system stability. Based on the constructed inequalities and the introduced delay-compensatory concept, sufficient stability and synchronization criteria for globally exponential synchronization of coupled neural networks are provided. To address the exponential synchronization problem in coupled neural networks. Utilizing delay-compensatory impulsive control and Razumikhin-type inequalities. The Lyapunov function for coupled neural networks with delays and integral terms exhibits exponential estimates.

Capital injections with negative surplus and delays: models and analysis

This work develops a new model to deal with the scenario that some companies can still run business even the surplus falls below zero temporarily. With such a scenario in mind, we allow the surplus process to continue in this negative-surplus period, during which capital injections will be ordered to assist in the stabilization of financial structure, until the financial status becomes severe enough to file bankruptcy. The capital injections will be modeled as impulse controls. By introducing the capital injections with time delays, optimal dividend payment and capital injection policies are considered. Using the dynamic programming approach, the value function obeys a quasi-variational inequality. With delays in capital injections, the company will be exposed to the risk of bankruptcy during the delay period. In addition, the optimal dividend payment and capital injection strategies should balance the expected cost of the possible capital injections and the time value of the delay periods. This gives rise to a stochastic control problem with mixed singular and delayed impulse controls. Under general assumptions, the lower capital injection barrier is determined, where bankruptcy occurs. The closed-form solution to the value function and corresponding optimal policies are obtained.