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Complexity
Volume 2017 (2017), Article ID 4107358, 12 pages
https://doi.org/10.1155/2017/4107358
Research Article

Analysis of a No Equilibrium Linear Resistive-Capacitive-Inductance Shunted Junction Model, Dynamics, Synchronization, and Application to Digital Cryptography in Its Fractional-Order Form

1Department of Mechanical and Electrical Engineering, Institute of Mines and Petroleum Industries, University of Maroua, P.O. Box 46, Maroua, Cameroon
2Department of Physics, Higher Teacher Training College, University of Bamenda, P.O. Box 39, Bamenda, Cameroon
3Research Group on Experimental and Applied Physics for Sustainable Development, Faculty of Science, Department of Physics, University of Dschang, P.O. Box 412, Dschang, Cameroon
4Laboratory of Electronics and Signal Processing Faculty of Science, Department of Physics, University of Dschang, P.O. Box 67, Dschang, Cameroon
5Laboratory of Modelling and Simulation in Engineering, Biomimetics and Prototypes (LaMSEBP) and TWAS Research Unit, Department of Physics, Faculty of Science, University of Yaoundé I, P.O. Box 812, Yaoundé, Cameroon

Correspondence should be addressed to Gaetan Fautso Kuiate

Received 16 June 2017; Accepted 9 August 2017; Published 12 October 2017

Academic Editor: Karthikeyan Rajagopal

Copyright © 2017 Sifeu Takougang Kingni et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A linear resistive-capacitive-inductance shunted junction (LRCLSJ) model obtained by replacing the nonlinear piecewise resistance of a nonlinear resistive-capacitive-inductance shunted junction (NRCLSJ) model by a linear resistance is analyzed in this paper. The LRCLSJ model has two or no equilibrium points depending on the dc bias current. For a suitable choice of the parameters, the LRCLSJ model without equilibrium point can exhibit regular and fast spiking, intrinsic and periodic bursting, and periodic and chaotic behaviors. We show that the LRCLSJ model displays similar dynamical behaviors as the NRCLSJ model. Moreover the coexistence between periodic and chaotic attractors is found in the LRCLSJ model for specific parameters. The lowest order of the commensurate form of the no equilibrium LRCLSJ model to exhibit chaotic behavior is found to be 2.934. Moreover, adaptive finite-time synchronization with parameter estimation is applied to achieve synchronization of unidirectional coupled identical fractional-order form of chaotic no equilibrium LRCLSJ models. Finally, a cryptographic encryption scheme with the help of the finite-time synchronization of fractional-order chaotic no equilibrium LRCLSJ models is illustrated through a numerical example, showing that a high level security device can be produced using this system.