5 citations · 8 across the 10 of their papers we have counts for
12 papers
An unbounded number of canard limit cycles in linear regularizations of piecewise linear systems
Renato Huzak, Otavio Henrique Perez
The purpose of this paper is to study the number of limit cycles of canard type in linear regularizations of piecewise linear systems with non-monotonic transition functions. Using…
Canard cycles of non-linearly regularized piecewise smooth vector fields
Peter De Maesschalck, Renato Huzak, Otavio Henrique Perez
The main purpose of this paper is to study limit cycles in non-linear regularizations of planar piecewise smooth systems with fold points (or more degenerate tangency points) and c…
Cyclicity of sliding cycles with singularities of regularized piecewise smooth visible-invisible two-folds
Jicai Huang, Renato Huzak, Otavio Henrique Perez +1
In this paper we study the cyclicity of sliding cycles for regularized piecewise smooth visible-invisible two-folds, in the presence of singularities of the Filippov sliding vector…
Fractal analysis of canard cycles and slow-fast Hopf points in piecewise smooth Liénard equations
Renato Huzak, Ansfried Janssens, Otavio Henrique Perez +1
The main goal of this paper is to give a complete fractal analysis of piecewise smooth (PWS) slow-fast Liénard equations. For the analysis, we use the notion of Minkowski dimension…
Sliding cycles of the regularized piecewise linear two-fold
Renato Huzak, Kristian Uldall Kristiansen
The goal of this paper is to study the number of sliding limit cycles of a regularized piecewise linear two-fold using the notion of slow divergence integral. We focus on li…
Slow divergence integral in regularized piecewise smooth systems
Renato Huzak, Kristian Uldall Kristiansen, Goran Radunović
In this paper we define the notion of slow divergence integral along sliding segments in regularized planar piecewise smooth systems. The boundary of such segments may contain dive…
Fractal analysis of hyperbolic saddles with applications
Vlatko Crnković, Renato Huzak, Maja Resman
In this paper we express the Minkowski dimension of spiral trajectories near hyperbolic saddles and semi-hyperbolic singularities in terms of the Minkowski dimension of intersectio…
Minkowski dimension and slow-fast polynomial Liénard equations near infinity
Peter De Maesschalck, Renato Huzak, Ansfried Janssens +1
In planar slow-fast systems, fractal analysis of (bounded) sequences in has proved important for detection of the first non-zero Lyapunov quantity in singular Hopf bifu…
Reading multiplicity in unfoldings from epsilon-neighborhoods of orbits
Renato Huzak, Pavao Mardešić, Maja Resman +1
We consider generic 1-parameter unfoldings of parabolic vector fields. It is known that the box dimension of orbits of their time-one maps is discontinuous at the bifurcation value…
Fractal codimension of nilpotent contact points in two-dimensional slow-fast systems
Peter De Maesschalck, Renato Huzak, Ansfried Janssens +1
In this paper we introduce the notion of fractal codimension of a nilpotent contact point , for , in smooth planar slowfast systems when the contact order $n…
The box dimension of degenerate spiral trajectories of a class of ordinary differential equations
Renato Huzak, Domagoj Vlah, Darko Žubrinić +1
In this paper we initiate the study of the box dimension of degenerate spiral trajectories of a class of ordinary differential equations. A class of singularities of focus type wit…
Jump-induced mixed-mode oscillations through piecewise-affine maps
Yiorgos Patsios, Renato Huzak, Nikola Popovic +1
Mixed-mode oscillations (MMOs) are complex oscillatory patterns in which large-amplitude relaxation oscillations (LAOs) alternate with small-amplitude oscillations (SAOs). MMOs are…