• M. S. Khan Department of Mathematics, Government National College, Karachi, Pakistan
  • M. J. Iqbal Institute of Space & Planetary Astrophysics, University of Karachi, Karachi, Pakistan


The science of chaos is a burgeoning field, and the available methods to investigate the existence of chaos in a time series are still being developed. Chaos is also characterized by a positive Lyapunov exponent, which can be thought of as a measure of the long-term unpredictability of the system; equilibrium and periodic attractors have a negative exponent, whereas a quasiperiodic attractor has an exponent of zero. During the last few decades there have emerged several attempts to use the paradigm of ‘chaos’ for a description and forecasting of climatic processes. The predictability of daily rainfall is the most difficult task due to the nonlinear complex climate’s dynamical system. This paper aims to investigate the existence of chaos in the time series of Lahore precipitation.


P. Grassberger and I. Procaccia, Phys.

Rev.Lett. 50 (1

D.J. Farmer and J.J. Sidorowich, Phys.Rev.

Lett. 59 (1987) 845.

M. Casdagli, Physica D 35 (1989) 335.

G. Sugihara and R.M. May, Nature

(1990) 734.

A. Wolf J.B

Vastano, Physica D 16 (1985) 285.

P. Grassberger and I. Procaccia, P

A 28 (1983c) 2591.

J. Theiler, S. Eu

Galdrikian and J.D. Farmer, Physica D 58

(1992) 77.

M. Palus, P

D. Prichard and J. Theiler, Physic

(1995) 476.

A. Hense, B

(1987) 34.

I. Rodrigue

and K.P. Georgakakos, Water Resour. Res.

, No. 7 (1989) 1667.

M.B. Sharifi, K.P.

I. Rodriguez, J. Atmos. Sci. 47 (1990) 888.

R. Berndtsson, K. Jinno, A. Kawamura,

Olsson and S. Xu, Trends Hydrol. 1 (1994)

A.W. J

(1994) 23.

C.E. Puente

Res. 32, No. 9 (1996) 2825.

T.B. Sangoyomi, U. La

Abarbanel, Water Resour. Res. 32, No. 1

(1996) 149.

A. Porporato

B 10 (1996) 1821.

A. Porporato and

Res. 33, No. 6 (1997) 1353.

B. Sivakumar, S.Y. Liong an

Am. Water Resour. Assoc. 34, No. 2 (1998)

B. Siv

Phoon, J. Hydrol. Eng. 4, No. 1 (1999a) 38.

H. Kantz, Phys. Lett. A 185 (1994) 77.

L. Feng, H.Y. Xing, G. Shirley and I. Ri

Complexity International 2 (1995), Monash

University, Australia .

E.N. Lorenz, J. Atmos.

S. Smale, Bulletin of American Mathematic

Society 73 (1967) 747.

D. Ruelle and F. Takens, Communications of

Mathematical Physics 20 (1971) 167 ; 23

(1971) 343.

J. Gleick, Chaos: Making a New Science.

Viking, New York (1987).

R.B. Blackman and J.W. Tukey, The

Measurement of Power Spectra from the

Point of View of Communication Engineering,

Dover Publications (1958) pp.190.

J.P. Eckmann and D Ruelle, Rev. Mod.

Phys. 57 (1985) 617.

H. Kantz and T. Schreiber, Nonlinear Time

Series Analysis, Cambridge University Press,

Cambridge (1997).

F. Takens, Detecting Strange Attractors in

Turbulence. Lecture Notes in Mathematics.

Vol. 898 (1981) Springer-Verlag, New York.

T. Sauer, J. Yorke and M. Casdagli,

Embedology. J. Stat. Phys. 65 (1991) 579.

A.M. Fraser and H.L. Swinney, Phys. Rev. A

(1986) 1134.

M.B. Kennel, R. Brown and H.D.I. Abarbanel,

Phys.Rev. A 45 (1992) 3403.

R. Hegger, H. Kantz and T. Schreiber, Chaos


P. Grassberger, R. Hegger, H. Kantz,

C. Schaffrath and T. Schreiber, Chaos 3

(1993) 127.

K. Jinno, S. Xu, R. Berndtsson,

A. Kawamura and M. Matsumoto,. J.

Geophys. Res. 100 (1995) 14773.

J.P. Eckmann, S. Oliffson Kamphorst and

D. Ruelle, Europhys. Lett. 4 (1987) 973.

J.P. Zbilut and C.L. Webber, Phys. Lett. A

(1992) 199.

N. Marwan, Encounters with Neighbours -

Current Developments of Concepts Based on

Recurrence Plots and their Applications.

Ph.D Thesis University of Potsdam (2003).

P.G. Drazin, Nonlinear Systems. Cambridge

University Press, New York (1994).

M. Sano and Y. Sawada, Phys. Rev. Lett. 55

(1985) 1082.

J.P. Eckmann O.S. Kamphorst, D. Ruelle and

S. Ciliberto, Phys. Rev. A. 34 (1986) 4971.




How to Cite

M. S. Khan and M. J. Iqbal, “INVESTIGATION OF CHAOS EXISTENCE IN THE TIME SERIES OF LAHORE PRECIPITATION”, The Nucleus, vol. 49, no. 1, pp. 1–9, Mar. 2012.




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