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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA


Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania


The Switching Function Projective Synchronization Dynamics of two Distinct Van der Pol-Duffing Oscillators with a Memristor-Duffing Oscillator

Discontinuity, Nonlinearity, and Complexity 10(3) (2021) 547--570 | DOI:10.5890/DNC.2021.09.014

Fuhong Min$^1$ , Chen Wei$^{1}$, Hanyuan Ma$^{1}$, Yiping Dou$^{1}$, Chunbiao Li$^{2}$

$^1$ School of Electrical and Automation Engineering, Nanjing Normal University, Nanjing, 210023, China

$^ 2$ School of Electrical and Information Engineering, Nanjing University of Information Science and Technology, Nanjing, 210044, China

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In this paper, through the discontinuous dynamical system theory, the system interactions of two distinct Van der Pol-Duffing oscillators and a Memristor-Duffing oscillator is discussed under a switching nonlinear controller with symbolic functions. The interaction conditions of three chaotic systems are treated as separation boundaries which is time-varying. Thus the corresponding motion domains are constrained by the boundaries and studied, and the analytical conditions for function project synchronization of three nonautonomous system via the switch-ability and attractivity of edge flows are developed. The control parameter maps with different invariant sets are also studied under the analytical conditions. The partial and full function projective synchronization are carried out via numerical simulations, and the interactions of the control parameters on the synchronization has been investigated. The switching projective synchronization are experimentally realized via analog circuit, and the experimental results validate the theoretical analysis.


This work is supported by National Natural Science Foundation of China under Grant No. 61971228, 61871230.


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