相互作用DBI暗能量模型的高维动力学系统稳定性分析  

Stability analysis on high dimensional dynamical system for DBI dark energy model with interaction

作　　者：吴亚波[1] 陈博海[1,2] 鲁军旺[3] 张楠 孙楚文[1] 守丽杰 徐海州 WU Yabo;CHEN Bohai;LU Junwang;ZHANG Nan;SUN Chuwen;SHOU Lijie;SHOU Lijie(School of Physics and Electronic Technology, Liaoning Normal University, Dalian 116029, China;Basic Science Department,North China Institute of Aerospace Engineering,Langfang 065000,China;School of Physics and Electronics,Qiannan Normal University for Nationalities,Duyun 558000,China)

机构地区：[1]辽宁师范大学物理与电子技术学院,辽宁大连116029 [2]北华航天工业学院基础科学部,河北廊坊065000 [3]黔南民族师范学院物理与电子科学学院,贵州都匀558000

出　　处：《辽宁师范大学学报（自然科学版）》2018年第1期30-39,共10页Journal of Liaoning Normal University:Natural Science Edition

基　　金：国家自然科学基金资助项目(11175077;11647167;11575075);辽宁省高校科学研究项目(L 201683666)

摘　　要：深入探讨相互作用狄拉克-玻恩-因费尔德(Dirac-Born-Infeld,简称DBI)暗能量模型的高维动力学系统稳定性问题.具体地,在五维相空间{X,Y,Z,Γ,Θ}中,求解动力学系统的临界点,并通过相关的宇宙学条件讨论其稳定性和吸引子行为以限制相互作用耦合参数β的取值范围.进一步,为了直观地描绘DBI暗能量模型的五维动力学系统的演化特性,在稳定点S3c附近通过选取多个初始值(取耦合常数β=2),画出了五维相空间{X,Y,Z,Γ,Θ}向二维{X,Y}和三维子空间{X,Y,Z}以及不存在相互作用(耦合常数为零)特殊情况的投影相图,以便考察稳定点S3c的吸引子行为,并与柯尼克姆(Kaeonikhom)的二维相空间{X,Y}和科普兰德(Copeland)的三维相空间{X,Y,Z}结果进行比较分析.最后,利用数值方法分别描绘出DBI暗能量宇宙密度参数Ω,态参数w,有效态参数weff和减速参数q的演化规律,给出它们的今天值,并与天文观测数据做比较.In this paper,the authors explored the stability of high dimensional dynamical system for Dirac-Born-Infeld(DBI)model with interaction.Concretely,the critical points are solved in5-dim phase space{X,Y,Z,Γ,Θ},the coupling parameterβis constrained,and the stability and the behavior of attractor are discussed by the cosmological constrains.Further,to depict the evolution of the DBI model in5\|dim dynamical system,the projections of phase diagram from5\|dim phase space{X,Y,Z,Γ,Θ}to2\|dim{X,Y}and3\|dim{X,Y,Z}space,also to the special case of no interaction,are drawn by choosing some initial points around S3c(taking the coupling parameterβ=2).So we can discuss the properties of the attractor S3c,and compare the results with ones in2\|dim{X,Y}and3\|dim{X,Y,Z}given by Kaeonikhom and Copeland,respectively.In addition,the evolutional laws of the density parameterΩ?,the equation of state w?,the effective equation of state w eff and the deceleration parameter q are described by numerical method.Finally,we can give their current values,and make comparison with the observation data from astronomy

关 键 词：暗能量 自洽动力学系统 稳定性 

分 类 号：O412.1[理学—理论物理]