‎hensel [k‎. ‎hensel‎, ‎deutsch‎. ‎math‎. ‎verein‎, ‎{6} (1897), ‎83-88.] discovered the $p$-adic number as a‎ ‎number theoretical analogue of power series in complex analysis‎. ‎fix ‎a prime number $p$‎. ‎for any nonzero rational number $x$‎, ‎there‎ ‎exists a unique integer $n_x inmathbb{z}$ such that $x = ‎frac{a}{b}p^{n_x}$‎, ‎where $a$ and $b$ are integers not divisible by ‎$p$‎. ‎then $|x...

The present work attracts attention to obtaining a new result of the periodic solution damped nonlinear Duffing oscillator and Klein–Gordon equation. It is known that frequency response equation in can be derived from homotopy analysis method only absence damping force. We suggest suitable scheme successfully produce without losing coefficient. novel strategy centered on establishing an alterna...

We treat a chain of oscillators with linear stiffness and internal external cubic non-linearities. The method harmonic balance is used to determine the non-linear modes Hamiltonian system. For each equilibrium point, stability analysis performed by means associated monodromy matrix. numerical results shows that branch points, limit points Neimark–Sacker bifurcations exist in aim paper study how...

existence of periodic solutions for non-linear third order autonomous differential equation (o.d.e.) has not been investigated to as large an extent as non-linear second order. the popular poincare-bendixon theorem applicable to second order equation is not valid for third order equation (see [3]). this conclusion opens a way for further investigation.

This paper treats the synchronization of a chain of non linear and uncertain model of non identical oscillators. Using the Lyapunov theory of stability, a dynamical controller guarantying the oscillators synchronization is determined. The problem of synchronization is transformed in a problem of asymptotic stabilization for a nonlinear system and then is formulated as a system of linear matrix ...

The behavior of arrays of coupled oscillators has been previously studied by computational solution of a set of nonlinear differential equations describing the time dependence of each oscillator in the presence of signals coupled from neighboring oscillators. The equations are sufficiently complicated in that intuitive understanding of the phenomena which arise is exceedingly difficult. We prop...

Existence of periodic solutions for non-linear third order autonomous differential equation (O.D.E.) has not been investigated to as large an extent as non-linear second order. The popular Poincare-Bendixon theorem applicable to second order equation is not valid for third order equation (see [3]). This conclusion opens a way for further investigation.