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.

On the maximal output set of fractional-order discrete-time linear systems

In this paper, we consider a linear discrete-time fractional-order system defined by \[\Delta ^{\alpha }x_ {k+1}=Ax_k+B u_k, \quad k \geq 0, \quad x_{0} \in \mathbb{R}^{n};\] \[y_{k}=Cx_k, \quad k \geq 0,\] where $A$, $B$ and $C$ are appropriate matrices, $x_{0}$ is the initial state, $\alpha$ is the order of the derivative, $y_k$ is the signal output and $u_k=K x_k$ is feedback control.  By defining the fractional derivative in the Grunwald–Letnikov sense, we investigate the characterization of the maximal output set, $\Gamma(\Omega)=\lbrace x_{0} \in \mathbb{R}^{n}/y_

State regulation of stability and effectiveness of money systems

The problems of stability providing by the way of using criterion of effectiveness of money systems models in the transitional and modern economys are researched. The methodological approaches with the increasing of effectiveness and stability of money systems through the possibility of achievement of certain economic and social priorities are considered.

Calculation of stable and unstable periodic orbits in a chopper-fed DC drive

It is well known that electric drives demonstrate various nonlinear phenomena.  In particular, a chopper-fed analog DC drive system is characterized by the route to chaotic behavior though period-doubling cascade.  Besides, the considered system demonstrates coexistence of several stable periodic modes within the stability boundaries of the main period-1 orbit.  We discover the evolution of several periodic orbits utilizing the semi-analytical method based on the Filippov theory for the stability analysis of periodic orbits.  We analyze, in particular, stable and unstable period-1, 2, 3 and

On the asymptotic output sensitivity problem for a discrete linear systems with an uncertain initial state

This paper studies a finite-dimensional discrete linear system whose initial state $x_0$ is unknown.  We assume that the system is augmented by two output equations, the first one $z_i$ being representing measurements made on the unknown state of the system and the other $y_i$ being representing the corresponding output.  The purpose of our work is to introduce two control laws, both in closed-loop of measurements $z_i$ and whose goal is to reduce asymptotically the effects of the unknown part of the initial state $x_0$.  The approach that we present consists of both th

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