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

We show that the iterative logarithm of each non-linear entire function is differentially transcendental over the ring of entire functions, and we give a sufficient criterion for such an iterative logarithm to be differentially transcendental over the ring of convergent power series. Our results apply, in particular, to the exponential generating function of a sequence arising from work of Shad...

This note presents closed-form formulas for determining the critical points of general ndimensional differential equations. The formulas do not require commutating the eigenvalues of the Jacobian of a system. Based on the Hurwitz criterion, explicit necessary and sufficient conditions are obtained. Particular attention is focused on Hopf and double Hopf bifurcations. A model of induction machin...

This paper presents a trajectory tracking control method for flexible space robot. The advantage of the method is that it is free from spill-over instability as it uses a robust overwhelming trajectory controller. The proposed controller is conceptualized for a single rotational degree of freedom case. The efficacy of the scheme is illustrated by simulation results. The stability analysis of th...

During the last years, the Internet Application (Remote Flexible Control and Instrumentation, Telecontrol...) has retained the attention of Control researchers for modeling and studying the congestion control of TCP/IP (Transfer Control Protocol/Internet Protocol) networks. The controllers proposed in the literature such as RED (Random Early Detection) or PID (Proportional Integrate Derivative)...

We enumerate Hurwitz orbits of shortest reflection factorizations an arbitrary element in the infinite family $G(m, p, n)$ complex groups. As a consequence, we characterize elements for which action is transitive and give simple criterion to tell when two belong same orbit. also quasi-Coxeter (those with factorization that generates whole group) n)$.

We establish a series of integral formulae involving the Hurwitz zeta function. Applications are given to integrals of Bernoulli polynomials, log Γ(q) and log sin(q).

Given a branched covering between closed connected surfaces, one can easily establish some relations between the Euler characteristic and orientability of the involved surfaces, the degree of the covering, the number of branching points, and the local degrees at these points. These relations can therefore be regarded as necessary conditions for the existence of the covering. A classical problem...

Making use of convolution product, we introduce a unified class of analytic functions with negative coefficients. Also, we obtain the coefficient bounds, extreme points and radius of starlikeness for functions belonging to the generalized class TP ( , ). Furthermore, partial sums fk(z) of functions f(z) in the class P  ( , ) are considered and sharp lower bounds for the ratios of real part of ...

A fractional order HIV model with both virus-tocell and cell-to-cell transmissions and therapy effect is investigated. The conditions for the existence of the equilibria are determined. Local stability analysis of the HIV model is studied by using the fractional Routh-Hurwitz stability conditions. We have generalized the integer LaSalle’s invariant theorem into fractional system and given some ...