TY - JOUR
T1 - A new chaotic oscillator - Properties, analog implementation, and secure communication application
AU - Nwachioma, Christian
AU - Humberto Perez-Cruz, J.
AU - Jimenez, Abimael
AU - Ezuma, Martins
AU - Rivera-Blas, R.
N1 - Publisher Copyright:
© 2013 IEEE.
PY - 2019
Y1 - 2019
N2 - This paper reports a new 3-dimensional autonomous chaotic system with four nonlinearities. The system is studied with respect to its numerical solutions in phase space, including sensitive dependence on initial conditions, equilibrium points, bifurcation, and maximal Lyapunov exponent. It is shown that the system is dissipative and has a fractional Lyapunov dimension. Besides, a basin of attraction is determined by the Newton-Raphson's method. To show its practicality, the new system is implemented by means of an analog electronic circuit. Aperiodicity of the experimental signal is verified by means of an improved power spectral density estimator, viz., the Welch's method. Also, the correlation dimension is estimated from the experimental time series with the result confirming that the responses are deterministic chaos. Finally, an electronic design of a secure communication application is carried out, wherein a nontrivial square wave is modulated by a master chaotic signal. The modulated signal is subsequently recovered by a slave system, and the fast convergence to zero of the information recovery error substantiates the effectiveness of the design.
AB - This paper reports a new 3-dimensional autonomous chaotic system with four nonlinearities. The system is studied with respect to its numerical solutions in phase space, including sensitive dependence on initial conditions, equilibrium points, bifurcation, and maximal Lyapunov exponent. It is shown that the system is dissipative and has a fractional Lyapunov dimension. Besides, a basin of attraction is determined by the Newton-Raphson's method. To show its practicality, the new system is implemented by means of an analog electronic circuit. Aperiodicity of the experimental signal is verified by means of an improved power spectral density estimator, viz., the Welch's method. Also, the correlation dimension is estimated from the experimental time series with the result confirming that the responses are deterministic chaos. Finally, an electronic design of a secure communication application is carried out, wherein a nontrivial square wave is modulated by a master chaotic signal. The modulated signal is subsequently recovered by a slave system, and the fast convergence to zero of the information recovery error substantiates the effectiveness of the design.
KW - Chaotic system
KW - Lyapunov spectrum
KW - analog circuit
KW - bifurcation analysis
KW - secure communication
KW - self-synchronization
UR - http://www.scopus.com/inward/record.url?scp=85060699021&partnerID=8YFLogxK
U2 - 10.1109/ACCESS.2018.2889964
DO - 10.1109/ACCESS.2018.2889964
M3 - Artículo
SN - 2169-3536
VL - 7
SP - 7510
EP - 7521
JO - IEEE Access
JF - IEEE Access
M1 - 8607984
ER -