This section deals with study the local stability character of the equilibrium point of Equation (1).
We will now consider two lemmas that will be used to prove the local stability character of the positive equilibrium points of system (6).
Marwan Aloqeili [1] investigated the stability character, semicycle behavior of the solution of the difference equation x n + 1 = x n − 1 / ( a − x n − 1 x n ).
In this section, we investigate the local stability character of the equilibrium point of Equation 1. Equation 1 has an equilibrium point.
We investigate the global stability character of the equilibrium points and the period-two solutions of, with positive parameters and nonnegative initial conditions.
We observe that their positions are affected by the radiation pressure forces, oblateness and the eccentricity of the orbits, but the stability character remains unchanged and are unstable.
Analytic criteria are developed which predict the existence and stability character of limit cycles as a function of the system parameters.
It demonstrates that the rotation of an asymmetric disc can change the nonlinear squeal behavior as well as the linear stability character drastically.
The special cases of (1) where the unique equilibrium changes its stability character from the local stability to repeller are cases where the Naimark-Sacker bifurcation occurs, see [8, 22], and these cases will be treated in an upcoming manuscript.
Subsequently, the surface of the core/shell NRs was functionalized by silica layer (CePO4 Tb@LaPO4@SiO2, core/shell/Si) to enhance the solubility and colloidal stability character in an aqueous and non-aqueous solvent.
