A Family of 1D Chaotic Maps without Equilibria

In this work, a family of piecewise chaotic maps is proposed. This parameterized by the nonlinear functions used for each piece mapping, which can be either symmetric or non-symmetric. Applying constraint on shape piece, generated have no equilibria and showcase behavior. thus belongs to category systems with hidden attractors. Numerous examples are provided, showcasing fractal-like, symmetrical patterns at interchange between non-chaotic Moreover, application proposed pseudorandom bit generator successfully performed.