In this paper we develop an arbitrary order Melnikov function to study limit cycles bifurcating
from a periodic submanifold for autonomous piecewise smooth differential systems in R n …

In this paper, we are interested in providing lower estimations for the maximum number of
limit cycles H (n) that planar piecewise linear differential systems with two zones separated …

We consider the well-known Sprott A system, which is a special case of the widely studied
Nosé–Hoover oscillator. The system depends on a single real parameter a, and for suitable …

Let the three-dimensional differential system defined by the jerk equation x ⃛=− ax ̈+ xx ̇
2− x 3− b x+ cx ̇, with a, b, c∈ R. When a= b= 0 and c< 0 the equilibrium point localized at …

The second part of Hilbert's sixteenth problem consists in determining the upper bound H (n)
for the number of limit cycles that planar polynomial vector fields of degree n can have. For …

In this paper we consider a simple dissipative oscillator, determined by a two-parameter
three-dimensional system of ordinary differential equations, obtained from the Nosé–Hoover …

We study a kind of better recurrence than Kolmogorov's one: periodicity recurrence, which
corresponds periodic solutions in distribution for stochastic differential equations. On the …

Recently, the higher order averaging method for studying periodic solutions of both Lipschitz
differential equations and discontinuous piecewise smooth differential equations was …

Recently sixteen 3-dimensional differential systems exhibiting chaotic motion and having no
equilibria have been studied, and it has been graphically observed that these systems have …

The Rössler system is characterized by a three-parameter family of quadratic 3D vector
fields. There exist two one-parameter families of Rössler systems exhibiting a zero-Hopf …