A strange novel chaotic system with fully golden proportion equilibria and its mobile microcomputer-based RNG application

Abstract

A strange novel three-dimensional quadratic continuous autonomous chaotic system with fully golden proportion equilibria is proposed. It has only seven terms, three quadratic nonlinearities and one parameter 'a'. The system equations have four equilibrium points and very interestingly all the equilibrium points have fully golden proportion values. Besides, this chaotic system has hidden amplitude control properties. The dynamic analyses of the system are presented such as equilibrium points, dissipativity, Lyapunov exponents, bifurcation diagrams, phase portraits and hidden amplitude control properties. Later, electronic circuit of the system is simulated in software and implemented in real environment Finally, microcomputer-based random number generator (RNG) application and its NIST-800-22 tests are executed as another real-time application.