# stability

## 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.

## Dynamical analysis of an HCV model with cell-to-cell transmission and cure rate in the presence of adaptive immunity

In this paper, we will study mathematically and numerically the dynamics of the hepatitis C virus disease with the consideration of two fundamental modes of transmission of the infection, namely virus-to-cell and cell-to-cell.  In our model, we will take into account the role of cure rate of the infected cells and the effect of the adaptive immunity.  The model consists of five nonlinear differential equations, describing the interaction between the uninfected cells, the infected cells, the hepatitis C virions and the adaptive immunity.  This immunity will be represented by the humoral and

## Mathematical modeling and analysis of Phytoplankton–Zooplankton–Nanoparticle dynamics

In this paper, we investigate the population dynamics of phytoplankton–zooplankton–nanoparticle model with diffusion and density dependent death rate of predator.  The functional response of predator in this model is considered as Beddington–DeAngelis type.  The stability analysis of the equilibrium points is observed by applying the Routh–Hurwitz criterion.  Numerical simulations are given to illustrate the theoretical results.

## Application of frequency stability criterion for analysis of dynamic systems with characteristic polynomials formed in j1/3 basis

This paper considers the stability of dynamical systems described by differential equations with fractional derivatives. In contrast to a number of works, where the differential equation describing the system may have a set of different values ​​of fractional derivatives, and the characteristic polynomial is formed on the basis of the least common multiple for the denominators of these indicators, this article proposes forming such a polynomial in a specific