Physica A 395 (2014) 112–120 Contents lists available at ScienceDirect Physica A journal homepage: www.elsevier.com/locate/physa Selection of minimal length of line in recurrence quantification analysis Behzad Babaei, Reza Zarghami * , Hossein Sedighikamal, Rahmat Sotudeh-Gharebagh, Navid Mostoufi Multiphase Processes Department, Oil and Gas Processing Centre of Excellence, School of Chemical Engineering, College of Engineering, University of Tehran, P.O. Box 11155/4563, Tehran, Iran highlights • It was revealed that Det of Lorenz time series has normal probability distribution. • The variance of Det versus l min has a convex parabolic shape. • The results prove that the value of l min = 2 is the best selection. • The optimum l min improves Det to distinguish between different dynamics of a system. article info Article history: Received 22 April 2012 Received in revised form 25 August 2013 Available online 26 October 2013 Keywords: Recurrence quantification analysis Minimal length of line Dynamic system abstract A qualitative analysis along with mathematical description was made on the selection of the optimal minimal length of line, l min , a crucial parameter in the recurrence quantification analysis (RQA). The optimum minimal length of line is defined as a value that enhances the capability of RQA variables (determinism, in this paper) to distinguish between different dynamic states of a system. It was shown that the determinism of the Lorenz time series has a normal distribution. The results indicated that the lowest possible value of the minimal length of line (i.e., l min = 2) is the best choice. This value provides the highest differentiation for determinism of the time series obtained from different dynamic states of the Lorenz system. The applicability of the results was verified by examining determinism for monitoring the fluidization hydrodynamics. © 2013 Elsevier B.V. All rights reserved. 1. Introduction Recurrence quantification analysis (RQA) has found special attention in the study of dynamic systems, in particular those that encompass complex dynamic features. Real world dynamic systems, like weather, the human body, stock price and industrial and engineering equipments, typically involve complex chaotic nonlinear behavior. These systems are governed by complex nonlinear dynamic relationships and are modeled by mathematical tools such as differential equations. Most of these systems have chaotic dynamics (i.e., they are highly sensitive to the initial condition) and their dynamic state cannot be predicted over a long time. Hence, real world dynamic systems usually are studied experimentally through time series evaluation of the measured signals of the underlying system. There are various statistical tools to study and characterize the dynamic features of time series [1]. Recurrence plot (RP) and RQA are unique and influential statistical tools for studying and characterizing of time series owing to applicability to both non-stationary and stationary time series [2,3]. For construction of the RP, any two points of underlying time series are compared to find whether their difference is smaller than the radius threshold or not. If the difference is less than the * Corresponding author. Tel.: +98 21 6696 7797; fax: +98 21 6646 1024. E-mail address: rzarghami@ut.ac.ir (R. Zarghami). 0378-4371/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.physa.2013.10.016