Recently, the logistic map is studied to analyse the impact on the chaotic dynamics of various iterated logistic maps using Picard, Mann, and many more. The purpose of this paper is to explore the behavior of a multi-scale population model, i.e. modified logistic map (Mod-LM) and chosen population proportion model, i.e. extended logistic map (Ex-LM) in an I-superior orbit using a bifurcation diagram. The additional parameters of Mod-LM and Ex-LM with the three-step iteration system, increase the degree of freedom which invariably enhances the stability of both the functions. A detailed study of possible scenarios has been conducted to discover the effect of each parameter to the fixed point and its location, periodic cycle, and stability condition by examining the corresponding bifurcation diagram. The experimental result is discussed in terms of convergence point and chaotic range of the given dynamical systems. 

A cryptosystem designed by using the combined features of fractal function and chaotic map, provides a secure and real time encryption environment. In this paper, a 2D-chaotic map is employed to create a chaotic key sequence to comply with the requirement of the key sensitivity. The set of initial values of the chaotic map has derived by iterating a conjugate transcendental fractal function (CTFF) i.e. z_(n+1)=conj(sin?(z_n^2 ) )+c. The fractal function produced three sets of initial values after iterating it using Picard, Mann, and Ishikawa iteration methods. Resultantly, three chaotic key sequences will be generated by executing 2D Sine Tent composite map (2D-STCM) for each set of initial values. Afterwards, perform zigzag scanning to each key stream to decorrelate the adjacent image pixels and combined them using XOR operation. By using a different summation of plain image pixels for each pixel encryption, improves the cryptosystem resistant against known/chosen-plaintext attack. Moreover, an encryption of a plain image pixel achieved using corresponding key sequence pixel and a previously ciphered pixel value. The proposed encryption/decryption scheme is evaluated using key space analysis, key sensitivity analysis, differential analysis and other statistical analyses. The performance result indicates the given scheme is efficient and reliable to be used with great potential for a secure image transmission application.

With the advancement in the network transmission media, need for secure data communication is strongly felt. Recently fractal based cryptosystem has become a topic of active research in computer network system because of its chaotic behavior. The proposed method utilizes the intrinsic relationship between Mandelbrot function and Julia function to develop a non-transitional key cryptosystem. The process starts with the formation of public key using superior Mandelbrot set with the help of few global as well as secret parameters on both sides. After exchanging public keys, both parties will generate their own private key using superior Julia set which will be same on both sides. The method is also implemented for Ishikawa iterated fractal function and subsequently carried out detailed analysis for both functions. The given cryptosystem utilizing two different iteration methods and improve the performance by increasing the encryption key up to 128 bits. As per experimental result and performance analysis, the key has large key space, high key sensitivity due to chaotic nature and efficient execution time which helps to achieve a secure communication network environment for data transmission.