Dynamics of an ecological prey–predator model based on the generalized Hattaf fractional derivative

In this paper, we propose and analyze a fractional prey–predator  model with generalized Hattaf fractional (GHF) derivative.  We prove that our proposed model is ecologically and mathematically well-posed.  Furthermore, we show that our model has three equilibrium points.  Finally, we establish the stability of these equilibria.

Поєднання алгоритму RSA і побітових операцій при шифруванні-дешифруванні зображень

Стосовно зображень розроблено модифікації алгоритму RSA такі, що зберігається криптографічна стійкість і забезпечується повна зашумленість зображення, з метою унеможливити використання методів візуальної обробки зображень.

For images modified RSA algorithm is developed such that stored cryptographic and secured full noisy image in order to prevent the use of methods of visual imaging.

Застосування алгоритму RSA у шифруванні і дешифруванні елементів локально-скінченного топологічного покриття зображення як компакту

Запропоновано застосування алгоритму RSA шифрування і дешифрування елементів локально скінченного топологічного покриття зображення, яке має чітко виділені внутрішні контури.

An application of RSA algorithm encryption and decryption of locally finite topological elements cover image that is clearly marked internal contours.

Effect of a nonlinear demand function on the dynamics of a fishery

In this work, we present and analyze a fishery model with a price variation.  We take into account the evolution in time of the fish biomass and the harvesting effort, while the price of fish is dependent on supply and demand.  Assuming that the price variation occurs at a fast time scale.  We assume that the stock and the effort evolution follow a slow time scale.

Basicity and Nucleophilicity Effect in Charge Transfer of AlH3-Base Adducts: Theoretical Approach

This study permits to explore the interactions involved in Lewis acid $\left(\mathrm{AlH}_3\right)$ and Lewis bases: $\mathrm{CO} ; \mathrm{H}_2\mathrm{O} ; \mathrm{NH}_3 ; \mathrm{PH}_3 ; \mathrm{PCl}_3 ; \mathrm{H}_2 \mathrm{S} ; \mathrm{CN}^{-} ; \mathrm{OH}^{-} ; \mathrm{O}_2^{-2} ; \mathrm{F}^{-} ; \mathrm{N}\left(\mathrm{CH}_3\right)_3 ; \mathrm{N}_2 ; \mathrm{N}_2 \mathrm{H}_4 ; \mathrm{N}_2 \mathrm{H}_2 ; \mathrm{C}_5 \mathrm{H}_5 \mathrm{N} ; \mathrm{C}_6 \mathrm{H}_{5^{-}}\mathrm{N}\mathrm{H}_2$.

Stability analysis and Hopf bifurcation of a delayed prey–predator model with Hattaf–Yousfi functional response and Allee effect

The Allee effect is an important phenomena in the context of ecology characterized by a correlation between population density and the mean individual fitness of a population.  In this work, we examine the influences of Allee effect on the dynamics of a delayed prey–predator model with Hattaf–Yousfi functional response.  We first prove that the proposed model with Allee effect is mathematically and ecologically well-posed.  Moreover, we study the stability of equilibriums and discuss the local existence of Hopf bifurcation.

Fractional derivative model for tumor cells and immune system competition

Modeling a dynamics of complex biologic disease such as cancer still present a complex dealing.  So, we try in our case to study it by considering the system of normal cells, tumor cells and immune response as mathematical variables structured in fractional-order derivatives equations which express the dynamics of cancer's evolution under immunity of the body.  We will analyze the stability of the formulated system at different equilibrium points.  Numerical simulations are carried out to get more helpful and specific outcome about the variations of the cancer's dynamics.

Dynamical behavior of predator–prey model with non-smooth prey harvesting

The objective of the current paper is to investigate the dynamics of a new predator–prey model, where the prey species obeys the law of logistic growth and is subjected to a non-smooth switched harvest: when the density of the prey is below a switched value, the harvest has a linear rate.  Otherwise, the harvesting rate is constant.  The equilibria of the proposed system are described, and the boundedness of its solutions is examined.  We discuss the existence of periodic solutions; we show the appearance of two limit cycles, an unstable inner limit cycle and a stable o

A continuous SIR mathematical model of the spread of infectious illnesses that takes human immunity into account

A mathematical model of infectious disease contagion that accounts for population stratification based on immunity criteria is proposed.  Our goal is to demonstrate the effectiveness of this idea in preventing different epidemics and to lessen the significant financial and human costs these diseases cause.  We determined the fundamental reproduction rate, and with the help of this rate, we were able to examine the stability of the free equilibrium point and then proposed two control measures.  The Pontryagin's maximum principle is used to describe the optimal controls,

Optimal control of tritrophic reaction–diffusion system with a spatiotemporal model

In this paper, we propose a new model of spatio-temporal dynamics concerning the tritrophic reaction-diffusion system by introducing Phytoplankton and Zooplankton.  We recall that the phytoplankton and zooplankton species are the basis of the marine food chain.  There is prey in each marine tritrophic system.  The main objective of this work is to control this species's biomass to ensure the system's sustainability.  To achieve this, we determine an optimal control that minimizes the biomass of super predators.