This paper presents the dynamic analysis of two discrete logistic chaotic maps versus the conventional map. The first map is the fractional logistic map with the extra degrees of freedom provided by the added number of variables. It has two more variables over the conventional one. The second map is the double-humped logistic map. It is a fourth-order map which increases the non-linearity over the conventional one. The dynamics of the three maps are discussed in details, including mathematical derivations of fixed points, stability analysis, bifurcation diagrams and the study of their chaotic regions. The chaotic behavior of the three maps, is investigated using the Maximum Lyapunov exponent (MLE). © 2017 IEEE.
Image encryption based on double-humped and delayed logistic maps for biomedical applications
This paper presents a secured highly sensitive image encryption system suitable for biomedical applications. The pseudo random number generator of the presented system is based on two discrete logistic maps. The employed maps are: the one dimensional double humped logistic map as well as the two-dimensional delayed logistic map. Different analyses are introduced to measure the performance of the proposed encryption system such as: histogram analysis, correlation coefficients, MAE, NPCR as well as UACI measurements. The encryption system is proven to be highly sensitive to ±0.001% perturbation of the logistic maps parameters. The system is tested on medical images of palm print as well as Parkinson disease MRI images. © 2017 IEEE.
Mathematical analysis of gene regulation activator model
This paper presents a complete analysis of the mathematical model of the gene regulation process. The model describes the induced gene expression under the effect of activators. The model differential equations are solved analytically, and the exact solution of the gene model is introduced. Moreover, a study of the model dynamics, including the fixed points and stability conditions are presented. The parameters effects on the phase plane portraits and the transient responses of the mRNA as well as the protein concentrations are intensively detailed. This work serves as a brick stone towards a complete model for a complete gene regulation biological process for future prediction and control of diseases at the genetic level. © 2018 IEEE.
Generalized delayed logistic map suitable for pseudo-random number generation
This paper presents the generalization of a delayed version of the logistic map. The effect of the added two general parameters is studied, which offers the option of having three different maps. The dynamic behavior of the vertical, zooming and the general map is analyzed. The study of the fixed points, stability ranges and bifurcation diagram of the delayed logistic map at hand is detailed in this work. The flow of the system behavior from stability to chaos is also presented with its transient response as well as its phase plane portraits. Moreover, using the general parameters, the option of designing any specific map is validated by some design examples, which makes it more optimal for any specific applications. The added general parameters offer increased randomness with controllability of the map design, making it more suitable for pseudo-random sequence generators which are used in image encryption algorithms and in secure communication transfer. © 2015 IEEE.
Fractional-Order Generalized Gene Regulation Model CCII-Based Practical Emulator
This paper presents a complete analysis of the mathematical model of the gene regulation process
Generalized fractional logistic map suitable for data encryption
This paper presents the generalization of a delayed version of the logistic map
Biomedical image encryption based on double-humped and fractional logistic maps
This paper presents a secured highly sensitive image encryption system suitable for biomedical applications
FPGA implementation of fractional-order Chua’s chaotic system
2018Abdelhamed M.A.Abu-Elyazeed M.F.Confrence PaperEl-Kader A.A.A.El-Maksoud A.J.A.Hassan B.G.Radwan A.G.Rihan N.G.Said L.A.Tolba M.F.
This paper introduces FPGA implementation of fractional order double scrolls chaotic system based on Chua circuit
Comparative study of fractional filters for Alzheimer disease detection on MRI images
This paper presents a comparative study of four fractional order filters used for edge detection
FPGA implementation of integer/fractional chaotic systems
2020Abd El-Kader A.A.Abd El-Maksoud A.J.Abu-Elyazeed M.F.Book ChapterHassan B.G.Radwan A.G.Rihan N.G.Said L.A.Tolba M.F.
Chaotic systems have remarkable importance in capturing some complex features of the physical process. Recently, fractional calculus becomes a vigorous tool in characterizing the dynamics of complex systems. The fractional-order chaotic systems increase the chaotic behavior in new dimensions and add extra degrees of freedom, which increase system controllability. In this chapter, FPGA implementation of different integer and fractional-order chaotic systems is presented. The investigated integer-order systems include Chua double scroll chaotic system and the modified Chua N-scroll chaotic system. The investigated fractional-order systems include Chua, Yalcin et al., Ozuogos et al., and Tang et al., chaotic systems. These systems are implemented and simulated based on the Grunwald–Letnikov (GL) definition with different window sizes. The parameters effect, along with different GL window sizes is investigated where some interesting chaotic behaviors are obtained. The proposed FPGA implementation utilizes fewer resources and has high throughput. Experimental results are provided on a digital oscilloscope. © Springer Nature Switzerland AG 2020.