A New Exponentially-Controlled Logistic Chaotic Map

Main Article Content

Jeerana Noymanee
Wimol San-Um


The typical logistic map has been utilized in a variety of applications such as in biological modeling and secure communications. Nonetheless, such a typical logistic map has only a single control parameter that sets all dynamic behaviors. This paper therefore introduces a new arbitrary power in the quadratic term in order to control stability of the system. The addition arbitrary power subsequently increases the degree of freedom of the logistic map and provides versatile responses as well as the flexibility of the system. Dynamic properties are described in terms of Cobweb plots, bifurcations, Lyapunov exponents, and chaotic waveforms in time domain. Experimental results utilize the Ardino microcontroller to generate chaotic waveforms with a relatively flat spectrum in frequency domain.


Download data is not yet available.

Article Details

Research Article


Yue Sun and Guangyi Wang, “A study on relations between loops in sequences generated by the logistic map over integers and real numbers”, IWSDA '09. Fourth International Workshop on Signal Design and its Applications in Communications, 19-23 Oct. 2009, pp. 165 - 168.

Xuefeng Zhang and Jiulun Fan, “Extended logistic chaotic sequence and its performance analysis”, Tsinghua science and Technology, Volume 12, July 2007, pp. 156-161.

Yue Sun and Guangyi Wang, “An Image Encryption Scheme Based on Modified Logistic Map”, 2011 Fourth International Workshop on Chaos-Fractals Theories and Applications (IWCFTA), 19-22 October 2011, pp. 179 - 182.

Shih-Liang Chen, TingTing Hwang and Wen-Wei Lin, “Randomness Enhancement Using Digitalized Modified Logistic Map”, IEEE Transactions on Circuits and Systems II: Express Briefs, Volume: 57, Issue: 12, Dec. 2010, pp. 996 – 1000.

E. Ott, Chaos in Dynamical Systems, Cambridge University Press, Cambridge, 2002.