A zero-Hopf equilibrium is an isolated equilibrium point whose eigenvalues are ±ωi≠0 and 0. In general for a such equilibrium there is no theory for knowing when it bifurcates some small-amplitude limit cycles moving the ...

In this paper we study the existence of transcritical and zero-Hopf bifurcations of the third-order ordinary differential equation x⃛ + ax¨ + bx˙ + cx- x2= 0 , called the Genesio equation, which has a unique quadratic ...

We characterize the values of the parameters for which a zero-Hopf equilibrium point takes place at the singular points, namely, O (the origin), P+, and P- in the FitzHugh-Nagumo system. We find two two-parameter families ...

We prove the existence of the classical Hopf bifurcation and of the zero-Hopf bifurcation in the Hindmarsh–Rose system. For doing this, some adequate change in parameters must be done in order that the computations become easier.

Nesse trabalho são apresentados alguns resultados importantes sobre bifurcações de codimensão dois de campos de vetores. O resultado principal dessa dissertação e o teorema que d a o diagrama de bifurcação e os retratos ...

In [Molaie et al., 2013] the authors provided the expressions of 23 quadratic differential systems in R3 with the unusual feature of having chaotic dynamics coexisting with one stable equilibrium point. In this paper, we ...

From the normal form of polynomial differential systems in R3 having a sphere as invariant algebraic surface, we obtain a class of quadratic systems depending on ten real parameters, which encompasses the well-known Sprott ...

In this paper, we consider a memristive circuit consisting of three elements: A passive linear inductor, a passive linear capacitor and an active memristive device. The circuit is described by a four-parameter system of ...

The first objective of this paper was to study the Darboux integrability of the polynomial differential system 'X PONTO' = y, 'Y PONTO' = z, 'Z PONTO' = −y − 'X POT.2' − xz + 3'Y POT.2' + a, and the second one is to ...