 , f We consider R T theory of gravity, where is the curvature scalar and T is the trace of the energy momentum tensor. Attention is attached to the special case,and two expressions are assumed for the func-parameters. We observe that by adjusting suitably these input parameters, energy conditions can be satisfied. Moreover, an analysis of the perturbations and stabilities of de Sitter solutions and power-law solutions is performed with the use of the two models. The results show that for some values of the input parameters, for which energy conditions are satisfied, de Sitter solutions and power-law solutions may be stables.

This paper considers nonlinear dynamics of plasma oscillations modeled by an anharmonic oscillator. These plasma oscillations are described by a nonlinear differential equation of the form ẍ + ͑1+x 2 ͒ẋ + x + x 2 + ␦x 3 = F cos ⍀t. The amplitudes of the forced harmonic, superharmonic, and subharmonic oscillatory states are obtained using the harmonic balance technique and the multiple time scales method. Admissible values of the amplitude of the external strength are derived. Bifurcation sequences displayed by the model for each type of oscillatory states are performed numerically through the fourth-order Runge-Kutta scheme.

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We analyze the stability and optimization of the synchronization process between two coupled self-excited systems modeled by the multi-limit cycles van der Pol oscillators through the case of an enzymatic substrate reaction with ferroelectric behavior in brain waves model. The one-way and two-way couplings synchronization are considered. The stability boundaries and expressions of the synchronization time are obtained using the properties of the Hill equation. Numerical simulations validate and complement the results of analytical investigations.

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