Effects Of Coupling On Synchronization In Lasers And Macroeconomic Game Systems

In this paper,we have studied the bi-directionally coupled semiconductor lasers system and the macroeconomic agent-based game system,respectively.Recent studies show that sufficiently strong couplings can cause synchronization,and the stronger coupling is,the better qualities of synchronization will have.The effects of the coupling strength on synchronization are complicated.In the former system,it shows that stronger couplings would cause outputs of lasers less synchronized with each other.In the latter system,there is no parameter that corresponds to the coupling strength.Synchronization in this model is achieved by introducing an appropriate time delay into the game strategy.After studying the details of the game strategy with time delay,we ascribe the synchronization to the change of phase transition properties.This result may provide a new way to explain synchronization phenomena.The study of synchronization in macroeconomic agent-based game system is a hot issue in the interdiscipline of physics and economics.Synchronization shown in this paper may gain an insight into the basic mechanism underlying the global downturn and cirsis waves in economic world.The main contributions are as follows:(1)In order to study the complex effects of the coupling strength on synchronization,numerical simulations are performed on the bi-directionally coupled three-semiconductor-lasers systems.We focus two different factors leading to synchronization and the coherence stack of these two factors.One of the factors is the coupling chain,the other is symmetric coupling architecture.The results indicate that the increased coupling strength cannot always promote synchronization.In some cases,it may even inhibit the synchronization.This inhibition is shown to be related to the destruction of symmetric coupling architecture.(2)In order to study the dynamic behaviors,numerical simulations are performed on MARK I agent-based model.We find that the synchronization phenomenon emerges only after a time delay with intermediate length is introduced,and the time delay weakens the efficiency of game strategy.This weakening effect is related to the occurrence of synchronization.We attribute the synchronization to the change of phase transition properties with the introduced time delay.The result is that synchronization concentrated in the critical zone of the continuous phase transition.In recent years,synchronization can always attract scientists' attention.This paper has discussed the complex effects of couping strength as well as synchronization phenomenon in systems where coupling strength can not be quantified explicitely.Our results may be potentially useful in future synchronization studies and provide a clue to improve the economic conditions.