Abstract. We consider a second-order equation of Duffing type. Bounds for the derivative of the restoring force are given which ensure the existence and uniqueness of a periodic solution. Furthermore, the unique periodic solution is asymptotically stable with sharp rate of exponential decay. In particular, for a restoring term independent of the variable t, a necessary and sufficient condition ...

A type of coupled map lattice (CML) is considered in this paper. What we want to do is to define the form of a traveling wave solution and to reveal its existence. Due to the infinite property of the problem, we have tried the periodic case, which can be dealt with on a finite set. The main approach for our study is the implicit existence theorem. The results indicate that if the parameters of ...

We present a direct method for reordering eigenvalues in the generalized periodic real Schur form of a regular K-cyclic matrix pair sequence (Ak, Ek). Following and generalizing existing approaches, reordering consists of consecutively computing the solution to an associated Sylvester-like equation and constructingK pairs of orthogonal matrices. These pairs define an orthogonal K-cyclic equival...

The spectral viscosity approximate solution of convex Hamilton–Jacobi equations with periodic boundary conditions is studied. It is proved in this paper that the approximation and its gradient remain uniformly bounded, formally spectral accurate, and converge to the unique viscosity solution. The L1-convergence rate of the order 1− ε∀ε > 0 is obtained.

In this paper, Newton Harmonic Balance Method (NHBM) is applied to obtain the analytical solution for an electron beam injected into a plasma tube where the magnetic field is cylindrical and increases towards the axis in inverse proportion to the radius. Periodic solution is analytically verified and consequently the relation between the Natural Frequency and the amplitude is obtained in an ana...

This paper is concerned with the dynamical stability analysis for almost periodic solution of memristive neural networks with time-varying delays. Under the framework of Filippov solutions, by applying the inequality analysis techniques, the existence and asymptotically almost periodic behavior of solutions are discussed. Based on the differential inclusions theory and Lyapunov functional appro...

We investigate a class of memristor-based shunting inhibitory cellular neural networks with leakage delays. By applying a new Lyapunov function method, we prove that the neural network which has a unique almost periodic solution is globally exponentially stable. Moreover, the theoretical findings of this paper on the almost periodic solution are applied to prove the existence and stability of p...