Dynamics of a fishery with nonlinear harvesting: control, price variation, and MSY

In this paper, we construct and analyse a new fishing mathematical model, which describes the time evolution of a fish stock, which is harvested by a fishing fleet, described by its fishing effort.  We consider that the price, which is given by the difference between supply and demand, is varying with respect to time.  For the harvesting function, we use the Holling II function.  On the other hand, we consider two different time scales: a fast one for the price variation and a slow one for fish stock and fishing effort variations.  We use an "aggregation of variables" m

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.

Ефект основності та нуклеофільності в перенесенні заряду адуктів AlH3-основ: теоретичний підхід

Це дослідження дозволяє вивчити взаємодію кислоти Льюїса $\left(\mathrm{AlH}_3\right)$ й основ Льюїса: $\mathrm{CO} ; \mathrm{H}_2\mathrm{O} ; \mathrm{NH}_3 ; \mathrm{PH}_3 ; \mathrm{PCl}_3 ; \mathrm{H}_2 \mathrm{S} ; \mathrm{CN}^{-} ; \mathrm{OH}^{-} ; \mathrm{O}_2^{-2} ; \mathrm{F}^{-} ; \mathrm{N}\left(\mathrm{CH}_3\right)_3 ; \mathrm{N}_2 ; \mathrm{N}_2 \mathrm{H}_4 ; \mathrm{N}_2 \mathrm{H}_2 ; \mathrm{C}_5 \mathrm{H}_5 \mathrm{N} ; \mathrm{C}_6 \mathrm{H}_{5^{-}}\mathrm{N}\mathrm{H}_2$.

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