This article studies the dynamics of a Gause-type predator-prey model with infectious disease in prey. The constructed is deterministic which assumes prey divided into two compartments i.e. susceptible and infected prey, both them are hunted by predator bilinearly. It investigated that there exist five biological equilibrium points such as all population extinction point, co-existence point. We...

We investigate stochastic averaging on the infinite time interval for a class of continuous-time nonlinear systems with stochastic perturbation and remove or weaken several restrictions present in existing results: global Lipschitzness of the nonlinear vector field, equilibrium preservation under the stochastic perturbation, global exponential stability of the average system, and compactness of...

We consider a mathematical model that describes the competition of three species for a single nutrient in a chemostat in which the dilution rate is assumed to be controllable by means of state dependent feedback. We consider feedback schedules that are affine functions of the species concentrations. In case of two species, we show that the system may undergo a Hopf bifurcation and oscillatory b...

Abstract We develop a new transmission model of COVID-19 in the presence waning immunity with isolation and vaccination humans. The spreading disease is determined by basic reproduction number (? 0 ). Based on mathematical analysis, we found that non-endemic equilibrium locally asymptotically stable when ? < 1 whereas endemic > 1. A numerical simulation used to show population dynamics. I...

Consensus is widely observed in nature as well as in society. Up to now, many works have focused on what kind of (and how) isolated single structures lead to consensus, while the dynamics of consensus in interdependent populations remains unclear, although interactive structures are everywhere. For such consensus in interdependent populations, we refer that the fraction of population adopting a...

In this paper, we present and analyze an SEIR Zika epidemic model. Firstly, we investigate the model with constant controls. The steady states of the model is found to be locally and globally asymptotically stable. Thereafter, we incorporate time dependent controls into the model in order to investigate the optimal effects of bednets, treatments of infective and spray of insecticides on the dis...

A controlled Lagrangian approach is presented for the stabilization of an inverted pendulum mounted on a cart. The stabilization strategy consists in forcing the closed-loop system to behave as an Euler-Lagrange system, with a fixed inertia matrix. For carrying it out, it is necessary to adequately shape the potential and kinetic energies of the closed-loop system. The idea behind this procedur...

This paper studies the problem of understanding noisy and structurally deformed two-dimensional images by means of abstractly defined neural works. First, in the framework of systems theory a neural network defined over a Hilbert space is introduced such that any given vectors in the Hilbert space are assigned to locally asymptotically stable fixed points of the network. Then, introducing struc...

The dynamic behavior of a predator-prey model with Holling type IV functional response is investigated with respect to impulsive control strategies. The model is analyzed to obtain the conditions under which the system is locally asymptotically stable and permanent. Existence of a positive periodic solution of the system and the boundedness of the system is also confirmed. Furthermore, numerica...