Evidence of low-dimensional dynamics in a trac noise time series V.K. Jain a, * , A.K. Srivastava a , Anup Das a , Vikas Rai b a School of Environmental Sciences, Jawaharlal Nehru University, New Delhi 110 067, India b Structural Biology Unit and Computer Centre, National Institute of Immunology, Aruna Asafali Road, New Delhi 110 067, India Accepted 16 February 2000 Abstract The noise level measurements were made at 10 s interval near a busy road which admits one-way trac only. The time series thus obtained was analysed using non-linear dynamical techniques. The results of the analysis suggest that the underlying dynamical process could be deterministic. It appears that the data support periodic and quasiperiodic attractors. The presence of colour ¯uctuations in the time series could be attributed to shuttling of the dynamics between these two attractors. Ó 2001 Elsevier Science Ltd. All rights reserved. 1. Introduction Vehicular trac is known to be the most prominent source of noise pollution in major cities around the world. It has been the focus of intense research activities [1±9] during the past two decades. A majority of these studies were undertaken with a view to assess the quality of the environment in urban areas. This necessitated monitoring of noise levels in residential, commercial, industrial and heavy trac zones. It is in this context that the noise and its spectral characteristics were investigated [10] at several important places and trac sites in Delhi, which has seen remarkable growth in road transport in recent years. Survey of noise inside various modes of transport has also been carried out in Delhi [11]. The scope of these studies is limited essentially to the objective of comparing the measured noise levels with permissible standards apart from gaining an insight into the spectral distribution of noise. In order that suitable remedial measures for controlling trac noise could be devised, it is imperative to analyse the high noise levels with associated ¯uctuations present at trac sites. The exact nature of the dynamical process responsible for these noise levels must be examined. It is generally believed that trac ¯ow is stochastic. This suggests that noise levels would also follow a stochastic law. However, the possi- bility that these noise level ¯uctuations can also be generated by a non-linear deterministic process should not be overlooked. These considerations have motivated us to ascertain the true nature of the underlying dynamical process generating the trac noise time series. We believe that by accurately analysing the trac noise, one can clearly know whether ¯uctuating noise can be brought down under the safe limits. For instance, if the time series is generated by a deterministic process, it can possibly be manipulated by controlling trac density (number of vehicles per hour) and composition (types of vehicles). On the other hand, a stochastic noise cannot be handled by any amount of human endeavour. www.elsevier.nl/locate/chaos Chaos, Solitons and Fractals 12 (2001) 859±864 * Corresponding author. Tel.: +91-011-6107676; fax: +91-011-6865886. E-mail address: vkjain@jnuniv.ernet.in (V.K. Jain). 0960-0779/01/$ - see front matter Ó 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 9 6 0 - 0 7 7 9 ( 0 0 ) 0 0 0 3 9 - 4