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, symmetrica...

The presence of the power-law memory is a significant feature many natural (biological, physical, etc.) and social systems. Continuous discrete fractional calculus instrument to describe behavior systems with memory. Existence chaotic solutions an intrinsic property nonlinear dynamics (regular fractional). Behavior can be very different from corresponding no Finding periodic points essential fo...

Chaotic behavior arising from very simple non-linear dynamical equation of logistic map makes it was used often in designing chaotic image encryption schemes. However, some properties of chaotic maps can also facilitate cryptanalysis especially when they are implemented in digital domain. Utilizing stable distribution of the chaotic states generated by iterating the logistic map, this paper pre...