Oscillation criteria for third order delay nonlinear differential equations

The purpose of this paper is to give oscillation criteria for the third order delay nonlinear differential equation \begin{equation*} \lbrack a_{2}(t)\{(a_{1}(t)(x^{\prime }(t))^{\alpha _{1}})^{\prime}\}^{\alpha _{2}}]^{\prime }+q(t)f(x(g(t)))=0, \end{equation*} via comparison with some first differential equations whose oscillatory characters are known. Our results generalize and improve some known results for oscillation of third order nonlinear differential equations. Some examples are given to illustrate the main results

Oscillation theorems concerning non-linear differential equations of the second order

This paper concerns the oscillation of solutions of the differential eq. [r,(t) ψ(x(t)) ƒ (x(t))] + q(t) φ (g(x(t)), r(t)ψ(x(t))=0 where uφ(u,v) > 0 for all u ≠ 0, xg(x)>0, xf(x)>0 for all x ≠ 0, ψ(x)>0 for all x ∈ R, r(t)>0 for t≥t0>0 and q is of arbitrary sign. Our results complement the results in [A.G. Kartsatos, On oscillation of nonlinear quations of second order, J. Math. Anal. Appl. 24 (1968), 665-668], and improve a number of existing oscillation criteria. Our main results are illustrated with examples

Hopf bifurcation and stability analysis for a delayed logistic equation with additive Allee effect

In this paper the linear stability of the delayed logistic equation with additive Allee effect is investigated. We also analyze the associated characteristic transcendental equation, to show the occurrence of Hopf bifurcation at the positive equilibrium. To determine the direction of Hopf bifurcation and the stability of bifurcating periodic solution, we use the normal form approach and a center manifold theorem. Finally, a numerical example is given to demonstrate the effectiveness of the theoretical analysis

An analytical study of the dynamic behavior of Lotka-Volterra based models of COVID-19

COVID-19 has become a world wide pandemic since its first appearance at the end of the year 2019. Although some vaccines have already been announced, a new mutant version has been reported in UK. We certainly should be more careful and make further investigations to the virus spread and dynamics. This work investigates dynamics in Lotka-Volterra based Models of COVID-19. The proposed models involve fractional derivatives which provide more adequacy and realistic description of the natural phenomena arising from such models. Existence and boundedness of non-negative solution of the fractional model is proved. Local stability is also discussed based on Matignon’s stability conditions. Numerical results show that the fractional parameter has effect on flattening the curves of the coexistence steady state. This interesting foundation might be used among the public health strategies to control the spread of COVID-19 and its mutated versions