Dynamics and bifurcations of nonsmooth systems: A survey
O Makarenkov, JSW Lamb - Physica D: Nonlinear Phenomena, 2012 - Elsevier
In this survey we discuss current directions of research in the dynamics of nonsmooth
systems, with emphasis on bifurcation theory. An introduction to the state-of-the-art (also for …
systems, with emphasis on bifurcation theory. An introduction to the state-of-the-art (also for …
Border-Collision Bifurcations in
DJW Simpson - siam REVIEW, 2016 - SIAM
For piecewise-smooth maps, new dynamics can be created by varying parameters such that
a fixed point collides with a surface on which the map is nonsmooth. If the map is continuous …
a fixed point collides with a surface on which the map is nonsmooth. If the map is continuous …
Sliding bifurcations of Filippov two stage pest control models with economic thresholds
S Tang, J Liang, Y Xiao, RA Cheke - SIAM Journal on Applied Mathematics, 2012 - SIAM
In order to control pests, a specific management strategy called the threshold policy is
proposed, which can be described by Filippov systems (or piecewise smooth systems). The …
proposed, which can be described by Filippov systems (or piecewise smooth systems). The …
Two-parameter discontinuity-induced bifurcations of limit cycles: Classification and open problems
P Kowalczyk, M di Bernardo… - … Journal of bifurcation …, 2006 - World Scientific
This paper proposes a strategy for the classification of codimension-two discontinuity-
induced bifurcations of limit cycles in piecewise smooth systems of ordinary differential …
induced bifurcations of limit cycles in piecewise smooth systems of ordinary differential …
Perturbation theory for non-smooth systems
MA Teixeira - Perturbation Theory: Mathematics, Methods and …, 2022 - Springer
Non-smooth dynamical system Systems derived from ordinary differential equations when
the non-uniqueness of solutions is allowed. In this article we deal with discontinuous vector …
the non-uniqueness of solutions is allowed. In this article we deal with discontinuous vector …
Nonsmooth homoclinic orbits, Melnikov functions and chaos in discontinuous systems
F Battelli, M Fečkan - Physica D: Nonlinear Phenomena, 2012 - Elsevier
We first study the problem of chaotic behaviour in time-perturbed discontinuous systems
whose unperturbed part has a piecewise C1 homoclinic solution transversally crossing the …
whose unperturbed part has a piecewise C1 homoclinic solution transversally crossing the …
SlideCont: An Auto97 driver for bifurcation analysis of Filippov systems
F Dercole, YA Kuznetsov - ACM Transactions on Mathematical Software …, 2005 - dl.acm.org
SLIDECONT, an AUTO97 driver for sliding bifurcation analysis of discontinuous piecewise-
smooth autonomous systems, known as Filippov systems, is described in detail. Sliding …
smooth autonomous systems, known as Filippov systems, is described in detail. Sliding …
[HTML][HTML] Bifurcations on a discontinuous Leslie–Grower model with harvesting and alternative food for predators and Holling II functional response
CC García - Communications in Nonlinear Science and Numerical …, 2023 - Elsevier
This paper proposes a mathematical model that describes the interaction of prey and
predators, assuming logistic growth for both species, harvesting and alternative food for …
predators, assuming logistic growth for both species, harvesting and alternative food for …
Bifurcation analysis of piecewise smooth ecological models
The aim of this paper is the study of the long-term behavior of population communities
described by piecewise smooth models (known as Filippov systems). Models of this kind are …
described by piecewise smooth models (known as Filippov systems). Models of this kind are …
Grazing-sliding bifurcations creating infinitely many attractors
DJW Simpson - International Journal of Bifurcation and Chaos, 2017 - World Scientific
As the parameters of a piecewise-smooth system of ODEs are varied, a periodic orbit
undergoes a bifurcation when it collides with a surface where the system is discontinuous …
undergoes a bifurcation when it collides with a surface where the system is discontinuous …