In this paper, He’s amplitude frequency formulation is used to obtain a periodic solution for a nonlinear oscillator with fractional potential. By calculation and computer simulations, compared with the exact solution shows that the result obtained is of high accuracy. Keywords—He’s amplitude frequency formulation; Periodic solution; Nonlinear oscillator; Fractional potential.

This paper is devoted to the study of the persistence of periodic solutions under perturbations in dynamical systems generated by evolutionary equations, which are not smoothing in finite time, but only asymptotically smoothing. Assuming that the periodic solution of the unperturbed system is non-degenerate, we want to prove the existence and uniqueness of a periodic solution for the perturbed ...

This paper is concerned with the extension of the concepts and theories of traveling wave solutions of time and space periodic monostable equations to time recurrent and space periodic ones. It first introduces the concept of generalized traveling wave solutions of time recurrent and space periodic monostable equations, which extends the concept of periodic traveling wave solutions of time and ...

The discrete analog of the well-known Favard Theorem states that the linear difference equation (1) x(t + 1) = A(t)x(t) + f(t) (t ∈ Z) with Bohr almost periodic coefficients admits at least one Bohr almost periodic solution if it has a bounded solution. The main assumption in this theorem is the separation among bounded solutions of the homogeneous equations (2) x(t + 1) = B(t)x(t), where B ∈ H...

We study solutions of almost periodic linear differential systems. This field is called the Favard theory what is based on the famous Favard result in [10] (see, e.g., [3, Theorem 1.2] or [28, Theorem 1]). It is a well-known corollary of the Favard (and the Floquet) theory that any bounded solution of a periodic linear differential system is almost periodic (see [12, Corollary 6.5] and [13] for...

⎯ In this paper, the existence, uniqueness and global attractivity are discussed on almost periodic solution of SICNNs (shunting inhibitory cellular neural networks) with continuously distributed delays. By using the fixed point theorem, differential inequality technique and Lyapunov functional method, giving the new ranges of parameters, several sufficient conditions are obtained to ensure the...

In this paper, we study dynamic commensalism model with nonmonotic functional response, density dependent birth rates on time scales and derive sufficient conditions for the permanence. We also establish the existence and uniform asymptotic stability of unique almost periodic positive solution of the model by using Lyapunov functional method.

in this paper, we present a new two-step trigonometrically fitted symmetric obrechkoff method. the method is based on the symmetric two-step obrechkoff method, with eighth algebraic order, high phase-lag order and is constructed to solve ivps with periodic solutions such as orbital problems. we compare the new method to some recently constructed optimized methods from the literature. the numeri...

We discuss the numerical solution of the output feedback optimal periodic control problem by using a gradient search based optimization approach. Extension of this approach to the simultaneous stabilization of periodic multimodels is also considered. For the evaluation of function and its gradient explicit expressions are derived which involve the numerical solution of a pair of discrete-time p...

Consider a one-mass system with two degrees of freedom, nonlin-early coupled, with parametric excitation in one direction. Assuming the internal resonance 1:2 and parametric resonance 1:2 we derive conditions for stability of the trivial solution by using both the harmonic balance method and the normal form method of averaging. If the trivial solution becomes unstable a stable periodic solution...