In this paper, the well-known Vallis model for El Niño is analyzed for the parameter condition
P≠ 0. The conditions for the stability of the equilibrium points are derived. The condition for …

We investigate a two-dimensional parameter-space of a three-parameter, three-variable,
continuous-time dynamical system, namely the Vallis model for El Niño phenomenon. We …

In this work we study the existence of new periodic solutions for the well knwon class of
Duffing differential equation of the form x+ cx+ a (t) x+ b (t) x3= h (t), where c is a real …

Abstract For m= 1, 2, 3, m= 1, 2, 3, we consider differential systems of the form x'\,=\, F_ 0 (t,
x)\,+\, i= 1^ m\, ε^ i F_ i (t, x)+ ε^ m+ 1 R (t, x, ε), x′= F 0 (t, x)+∑ i= 1 m ε i F i (t, x)+ ε m+ 1 R …

Vallis proposed a simple model for El-Niño weather phenomenon (referred as Vallis system)
by adding an additional parameter p to the Lorenz system. He showed that the chaotic …

In this paper, some aspects on the periodic solutions of the extended Duffing–Van der Pol
oscillator are discussed. Doing different rescaling of the variables and parameters of the …

The Darboux polynomials and invariant algebraic surfaces of the Vallis system were
investigated. In the proofs, the weighted homogeneous polynomials and the characteristic …

DETECTING PERIODIC ORBITS IN SOME 3D CHAOTIC QUADRATIC POLYNOMIAL
DIFFERENTIAL SYSTEMS 1. Introduction Finding periodic orbits o Page 1 h tt p://ww w .gs du …

The method of averaging is a classical tool allowing us to study the dynamics of the non-
linear differential systems under periodic forcing. The method of averaging has a long …

In many engineering problems, when studying the existence of periodic solutions to a
nonlinear system with a small parameter via the local averaging theorem, it is necessary to …