Abstract
This work presents a new four-dimensional autonomous hyperchaotic system based on Méndez-Arellano-Cruz-Martínez (MACM) 3D chaotic system. Analytical and numerical studies of the dynamic properties are conducted for the new hyperchaotic system (NHS) in its continuous version (CV), where the Lyapunov exponents are calculated. The CV of the NHS is simulated and implemented using operational amplifiers (OAs), whereas the Discretized Version (DV) is simulated and implemented in real-time. Besides, a novel study of the algorithm performance of the proposed DV of NHS is conducted with the digital-electronic implementation of the floating-point versus Q1.15 fixed-point format by using the Digital Signal Processor (DSP) engine of a 16-bit dsPIC microcontroller and two external dual digital to analog converters (DACs) in an embedded system (ES).
Highlights
In recent years, the potential applications of chaotic systems have attracted attention as an interesting nonlinear phenomenon, since the chaotic properties are highly desired in several areas of science and engineering such as high sensitivity to initial conditions, high entropy, topology complexity, ergodicity [1,2,3], among others
We firstly introduce a new 4D hyperchaotic system (NHS) via modifying 3D MACM system inspired by the above works [32]
The results showed that new hyperchaotic attractor presents two positive Lyapunov exponents, an unstable equilibrium saddle-point at the origin, and it is flexible and robust which allows obtaining different hyperchaotic and chaotic behavior
Summary
The potential applications of chaotic systems have attracted attention as an interesting nonlinear phenomenon, since the chaotic properties are highly desired in several areas of science and engineering such as high sensitivity to initial conditions, high entropy, topology complexity, ergodicity [1,2,3], among others. The electronic digital implementation of chaotic systems has attracted the attention for the community scientific for the several applications in engineering, e.g., the cryptosystems—where the main encryption process is based on chaos—are designed considering statistical and security tests, even if the cryptosystem has good performance, the computing capacity on embedded systems continues being a challenge for designers [9,10,14,17]. Only two nonlinearities, flexible and robust, one unstable equilibrium saddle-point, and low-cost electronic implementation for the continuous and discretized versions are the main novelties of the proposed hyperchaotic system All these features result in a highly attracting digital implementation, such as low complexity time, high iterations per second (ips) where chaos is preserved, and it may be of great interest for engineering applications such as chaos-based cryptography, biometric systems, telemedicine, and secure communications.
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