A modified simple logistic chaotic map through exponential controller in nonlinear term

A typical logistic map has been utilized in a variety of applications such as in biological modeling and secure communications. Nonetheless, such a typical logistic map has only a single control parameter that sets all dynamic behaviors. This paper therefore introduces a new arbitrary power in the quadratic term in order to control stability of the system. The addition arbitrary power subsequently increases the degree of freedom of the logistic map and provides versatile responses as well as the flexibility of the system. Dynamic properties are described in terms of Cobweb plots, bifurcations, Lyapunov exponents, and chaotic waveforms in time domain. Experimental results utilize the Arduino microcontroller to generate chaotic waveforms with a relatively flat spectrum in frequency domain. The application in random-bit generator that passes all NIST standard tests is also involved.