Fractional-order two-component oscillator: stability and network synchronization using a reduced number of control signals

Romanic Kengne, Robert Tchitnga, Alain Kammogne Soup Tewa, Grzegorz Litak (), Anaclet Fomethe and Chunlai Li
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Romanic Kengne: Research Group on Experimental and Applied Physics for Sustainable Development, Faculty of Science, Department of Physics, University of Dschang
Robert Tchitnga: Research Group on Experimental and Applied Physics for Sustainable Development, Faculty of Science, Department of Physics, University of Dschang
Alain Kammogne Soup Tewa: Laboratory of Electronics and Signal Processing Faculty of Science, Department of Physics, University of Dschang
Grzegorz Litak: Lublin University of Technology, Faculty of Mechanical Engineering
Anaclet Fomethe: Laboratoire de Mécanique et de Modélisation des Systèmes, L2MS, Department of Mathematics and Computer Science, Faculty of Science, University of Dschang
Chunlai Li: College of Physics and Electronics, Hunan Institute of Science and Technology Yueyang

The European Physical Journal B: Condensed Matter and Complex Systems, 2018, vol. 91, issue 12, 1-19

Abstract: Abstract In this paper, a fractional-order version of a chaotic circuit made simply of two non-idealized components operating at high frequency is presented. The fractional-order version of the Hopf bifurcation is found when the bias voltage source and the fractional-order of the system increase. Using Adams–Bashforth–Moulton predictor–corrector scheme, dynamic behaviors are displayed in two complementary types of stability diagrams, namely the two-parameter Lyapunov exponents and the isospike diagrams. The latest being a more fruitful type of stability diagrams based on counting the number of spikes contained in one period of the periodic oscillations. These two complementary types of stability diagrams are reported for the first time in the fractional-order dynamical systems. Furthermore, a new fractional-order adaptive sliding mode controller using a reduced number of control signals was built for the stabilization of a fractional-order complex dynamical network. Two examples are shown on a fractional-order complex dynamical network where the nodes are made of fractional-order two-component circuits. Firstly, we consider an ideal channel, and secondly, a non ideal one. In each case, increasing of the coupling strength leads to the phase transition in the fractional-order complex network. Graphical abstract

Keywords: Statistical; and; Nonlinear; Physics (search for similar items in EconPapers)
Date: 2018
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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DOI: 10.1140/epjb/e2018-90362-7

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