Chaos theory attempts to explain the result of a system that is sensitive to initial conditions, complex, and shows an unpredictable behaviour. Chaotic systems are sensitive to any change or changes in the initial condition(s) and are unpredictable in the long term. Chaos theory are implementing today in many different fields of studies. In this research, we propose a new one-dimensional Triangular Chaotic Map (TCM) with full intensive chaotic population. TCM chaotic map is a one-way function that prevents the finding of a relationship between the successive output values and increases the randomness of output results. The tests and analysis results of the proposed triangular chaotic map show a great sensitivity to initial conditions, have unpredictability, are uniformly distributed and random-like and have an infinite range of intensive chaotic population with large positive Lyapunov exponent values. Moreover, TCM characteristics are very promising for possible utilization in many different study fields.
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