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Control of Divergence in an Extended Invertible Logistic Map

School of Electrical and Information Engineering of Jinan University, 206 Qianshan Road, Zhuhai 519070, Guangdong, P. R. China

E-mail Address: tgqluyp@jnu.edu.cn

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Mantas Landauskas

Center for Nonlinear Systems, Kaunas University of Technology, Studentu 50-147, Kaunas LT-51368, Lithuania

E-mail Address: mantas.landauskas@ktu.lt

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, and

Minvydas Ragulskis

http://orcid.org/0000-0002-3348-9717

School of Electrical and Information Engineering of Jinan University, 206 Qianshan Road, Zhuhai 519070, Guangdong, P. R. China

Center for Nonlinear Systems, Kaunas University of Technology, Studentu 50-147, Kaunas LT-51368, Lithuania

E-mail Address: minvydas.ragulskis@ktu.lt

Corresponding author.

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https://doi.org/10.1142/S0218127418501298Cited by:4 (Source: Crossref)

Abstract

The extended invertible Logistic map and its properties are investigated in this paper. It is demonstrated that initial conditions of the extended invertible Logistic map can yield trajectories of three different types. Dedicated algorithms are used to prove the existence of transient Wada-type boundaries in the phase plane of initial conditions. An adaptive control technique for the temporary control of the divergence of the extended invertible Logistic map is proposed. This control technique is based on short impulses and exploits the properties of the Wada-type boundaries. Computational experiments are used to illustrate the efficacy of the proposed technique.

Keywords:

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