# stability

## 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

## Study of the processing of small diagnostic creations on a fluid sourcing by spiral survivals

The article considers the features of the drilling process where there is a change in temperature, hole diameter, and displacement relative to the axis and the impact on the tool, when machining holes with high-speed steel drills there is wear of the transverse edge which is completely rounded to create a conical surface. There is a decrease in the negative value of the front corners on the transverse edge of the decrease in axial force, which led to a decrease in the intensity of wear of the transverse edge.

## Positivity and stability of descriptor linear systems with interval state matrices

The positivity and asymptotic stability of descriptor linear continuous-time and discrete-time systems with interval state matrices and interval polynomials are investigated. Necessary and sufficient conditions for the positivity of descriptor continuous-time and discrete-time linear systems are established. It is shown that the convex linear combination of polynomials of positive linear systems is also the Hurwitz polynomial. The Kharitonov theorem is extended to the positive descriptor linear systems with interval state matrices.