A Dynamic-Order Fractional Dynamic System

• 来源期刊: 中国物理快报（英文版）
• 年，卷（期）: 2013,（4）
• 页码范围: 154-157
• 页数: 4页
• 语种: 英文
• DOI: 10.1088/0256-307X/30/4/046601

摘要

In the last decades,fractional dynamic systems have received great success in the analysis of anomalous diffusion,[1-4] viscoelastic rheology,[5,6] control systems,[7-9] wave dissipation in human tissue,electrochemical corrosion process,[10] etc.[11-13] More recently,a number of theoretical and applied researches in the physical field have attracted increasing attention to variable-order fractional dynamic systems,which is a natural extension of fractional dynamic systems.[14,15,16] A variable-order fractional dynamic system may also be a promising approach to explore the physical mechanism of multi-system interaction.Especially,the behavior of a dynamic system may change with the evolution of other dynamic systems in multi-system physical processes.How can we characterize the interaction effect between these dynamic systems? Establishing a system of equations which include intricate interaction terms will cause great difficulties in modeling and computation.Even worse,since they may miss capturing the critical physical mechanism of the considered problem,the established model may produce incorrect results which greatly deviate from experimental results or field measurement data.Meanwhile,researchers have confirmed that the differential orders in some fractional dynamic systems are not constant and are often functions of other variables or system outputs.[16,17] For instance,Gl(o)ckle and Nonnenmacher[18] have found that the differential order of protein relaxation is a function of temperature.Therefore,when exploring the physical mechanism of a variable-order fractional dynamic system,another dynamic system should usually be studied.For simplicity,we name this type of variable-order fractional dynamic system the dynamic-order fractional dynamic system.From a physical viewpoint,the differential order should be called the dynamicorder in many fractional systems.