{"title":"具有相对利润委托的离散分数阶库诺二元垄断博弈模型:稳定性、分岔、混沌、0-1 检验和控制","authors":"Senol Kartal","doi":"10.1016/j.cam.2024.116284","DOIUrl":null,"url":null,"abstract":"<div><div>Due to the memory effect, fractional order dynamical systems provide more realistic results compared with ordinary counterparts. In this study, we consider a Cournot-duopoly game model with relative profit delegation in the sense of Caputo fractional derivative. To describe richer dynamical behavior such as chaos in the model, a discrete dynamical system is needed. As a result of the discretization method based on the use of piecewise constant arguments, we obtain a two dimensional system of difference equations. The stability conditions of all equilibrium points of the discrete dynamical system are given comprehensively. The existence of the flip bifurcation in the system has been demonstrated theoretically. Lyapunov exponents and 0–1 test chaos imply that chaotic structures are formed as a result of this bifurcation. In addition, we present the chaos control technique such as Pyragas method to eliminate chaos in the model. All theoretical results dealing with the stability, bifurcation and chaos in the model are stimulated by numerical simulations.</div></div>","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A discrete fractional order cournot duopoly game model with relative profit delegation: Stability, bifurcation, chaos, 0-1 testing and control\",\"authors\":\"Senol Kartal\",\"doi\":\"10.1016/j.cam.2024.116284\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>Due to the memory effect, fractional order dynamical systems provide more realistic results compared with ordinary counterparts. In this study, we consider a Cournot-duopoly game model with relative profit delegation in the sense of Caputo fractional derivative. To describe richer dynamical behavior such as chaos in the model, a discrete dynamical system is needed. As a result of the discretization method based on the use of piecewise constant arguments, we obtain a two dimensional system of difference equations. The stability conditions of all equilibrium points of the discrete dynamical system are given comprehensively. The existence of the flip bifurcation in the system has been demonstrated theoretically. Lyapunov exponents and 0–1 test chaos imply that chaotic structures are formed as a result of this bifurcation. In addition, we present the chaos control technique such as Pyragas method to eliminate chaos in the model. All theoretical results dealing with the stability, bifurcation and chaos in the model are stimulated by numerical simulations.</div></div>\",\"PeriodicalId\":2,\"journal\":{\"name\":\"ACS Applied Bio Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.6000,\"publicationDate\":\"2024-09-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACS Applied Bio Materials\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0377042724005326\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATERIALS SCIENCE, BIOMATERIALS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0377042724005326","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
A discrete fractional order cournot duopoly game model with relative profit delegation: Stability, bifurcation, chaos, 0-1 testing and control
Due to the memory effect, fractional order dynamical systems provide more realistic results compared with ordinary counterparts. In this study, we consider a Cournot-duopoly game model with relative profit delegation in the sense of Caputo fractional derivative. To describe richer dynamical behavior such as chaos in the model, a discrete dynamical system is needed. As a result of the discretization method based on the use of piecewise constant arguments, we obtain a two dimensional system of difference equations. The stability conditions of all equilibrium points of the discrete dynamical system are given comprehensively. The existence of the flip bifurcation in the system has been demonstrated theoretically. Lyapunov exponents and 0–1 test chaos imply that chaotic structures are formed as a result of this bifurcation. In addition, we present the chaos control technique such as Pyragas method to eliminate chaos in the model. All theoretical results dealing with the stability, bifurcation and chaos in the model are stimulated by numerical simulations.