38 citations · 81 across the 8 of their papers we have counts for
8 papers
Detecting Limit Tori in Non-Smooth Systems: An Analytic Approach with Applications to 3D Piecewise Linear Systems
Murilo R. Cândido, Douglas D. Novaes, Joan S. G. Rivera
This work investigates a class of non-autonomous -periodic piecewise smooth differential systems and their associated time- maps. Our main result provides an analytical appro…
Invariant Tori and Periodic Orbits in the FitzHugh-Nagumo System
Murilo R. Cândido, Douglas D. Novaes, Nasrin Sadri
The FitzHugh-Nagumo system is a -parameter family of D vector field used for modeling neural excitation and nerve impulse propagation. The origin represents a Hopf-zero equil…
On the stability of smooth branches of periodic solutions for higher order perturbed differential equations
Murilo R. Cândido, Douglas D. Novaes
The averaging method combined with the Lyapunov-Schmidt reduction provides sufficient conditions for the existence of periodic solutions of the following class of perturbative -…
A mechanism for detecting normally hyperbolic invariant tori in differential equations
Pedro C. C. R. Pereira, Douglas D. Novaes, Murilo R. Cândido
Determining the existence of compact invariant manifolds is a central quest in the qualitative theory of differential equations. Singularities, periodic solutions, and invariant to…
Zero-Hopf bifurcation in the general Van der Pol-Duffing equation
Murilo Cândido, Claudia Valls
We study analytically the coexistence of multiple periodic solutions and invariant tori in the general Van der Pol-Duffing oscillator equations. We use several results related to t…
Periodic solutions and invariant torus in the Rössler System
Murilo R. Cândido, Douglas D. Novaes, Claudia Valls
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 equi…
On the torus bifurcation in averaging theory
Murilo R. Cândido, Douglas D. Novaes
In this paper, we take advantage of the averaging theory to investigate a torus bifurcation in two-parameter families of 2D nonautonomous differential equations. Our strategy consi…
Persistence of periodic solutions for higher order perturbed differential systems via Lyapunov-Schmidt reduction
Murilo R. Cândido, Jaume Llibre, Douglas D. Novaes
In this work we first provide sufficient conditions to assure the persistence of some zeros of functions having the form $$g(z,\varepsilon)=g_0(z)+\sum_{i=1}^k \varepsilon^i g_i(z)…