bifurcation

Antinomical Nature of Artificial Law

Circumstances of earthly life, various vital factors that took place in society, the national state, and interstate relations require specific regulation. The creative atmosphere of a person generates a powerful set of laws. Their number is constantly growing, which requires constant attention to quality, as insoluble, insurmountable contradictions appear. Knowing these contradictions is inextricably linked with doubts.

An epidemic model with viral mutations and vaccine interventions

In this paper, we introduce a two-strain SIR epidemic model with viral mutation and vaccine administration.  We discuss and analyze the existence and stability of equilibrium points.  This model has three types of equilibrium points, namely disease-free equilibrium, dominance equilibrium point of strain two, and coexistence endemic equilibrium point.  The local stability of the dominance equilibrium point of strain two and coexistence endemic equilibrium point are verified by using the Routh--Hurwitz criteria, while for the global stability of the dominance equilibrium point of strain two,

Dynamical behavior of predator–prey model with non-smooth prey harvesting

The objective of the current paper is to investigate the dynamics of a new predator–prey model, where the prey species obeys the law of logistic growth and is subjected to a non-smooth switched harvest: when the density of the prey is below a switched value, the harvest has a linear rate.  Otherwise, the harvesting rate is constant.  The equilibria of the proposed system are described, and the boundedness of its solutions is examined.  We discuss the existence of periodic solutions; we show the appearance of two limit cycles, an unstable inner limit cycle and a stable o