Integrable 2D and 3D piecewise smooth vector fields with chaotic behavior and preserving energy or not

被引：2
作者：
Carvalho, Tiago [1 ]
机构：
[1] FFCLRP USP, BR-14040901 Ribeirao Preto, SP, Brazil
来源：
PHYSICA D-NONLINEAR PHENOMENA | 2024年 / 463卷
基金：
巴西圣保罗研究基金会;
关键词：
Piecewise smooth vector field; Chaos; First integrals; DYNAMIC-MODEL; MINIMAL SETS; THERAPY; HIV-1;
D O I：
10.1016/j.physd.2024.134161
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we exhibit 2D and 3D piecewise smooth vector fields that have, at the same time, first integrals and chaotic behavior. The fact of existing first integrals means that the trajectories are tangent to foliations. Also, in some of these examples the trajectories live in an unique level of the first integrals, and so the system preserves energy, and in other cases the trajectories visit distinct levels of the first integrals and the system does not preserves the energy.
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页数：7
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共 33 条
[1]   CD4-guided scheduled treatment interruptions compared with continuous therapy for patients infected with HIV-1:: results of the Staccato randomised trial [J].
Ananworanich, Jintanat ;
Gayet-Ageron, Angele ;
Le Braz, Michelle ;
Prasithsirikul, Wisit ;
Chetchotisakd, Ploenchan ;
Kiertiburanakul, Sasisopin ;
Munsakul, Warangkana ;
Raksakulkarn, Phitsanu ;
Tansuphasawasdikul, Somboon ;
Sirivichayakul, Sunee ;
Cavassini, Matthias ;
Karrer, Urs ;
Genne, Daniel ;
Nueesch, Reto ;
Vernazza, Pietro ;
Bernasconi, Enos ;
Leduc, Dominic ;
Satchell, Claudette ;
Yerly, Sabine ;
Perrin, Luc ;
Hill, Andrew ;
Perneger, Thomas ;
Phanuphak, Praphan ;
Furrer, Hansjakob ;
Cooper, David ;
Ruxrungtham, Kiat ;
Hirschel, Bernard .
LANCET, 2006, 368 (9534) :459-465
[2]  
Brogliato B, 1999, Nonsmooth Mechanics: Models, Dynamics and Control, Vsecond, P552, DOI 10.1007/978-1-4471-0557-2
[3]   ON POINCARE BENDIXSON THEOREM AND NON-TRIVIAL MINIMAL SETS IN PLANAR NONSMOOTH VECTOR FIELDS [J].
Buzzi, Claudio A. ;
Carvalho, Tiago ;
Euzebio, Rodrigo D. .
PUBLICACIONS MATEMATIQUES, 2018, 62 (01) :113-131
[4]   Chaotic planar piecewise smooth vector fields with non-trivial minimal sets [J].
Buzzi, Claudio A. ;
De Carvalho, Tiago ;
Euzebio, Rodrigo D. .
ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2016, 36 :458-469
[5]   Global Analysis of a piecewise smooth epidemiological model of COVID-19 [J].
Carvalho, Tiago ;
Cristiano, Rony ;
Rodrigues, Diego S. ;
Tonon, Durval J. .
NONLINEAR DYNAMICS, 2021, 105 (04) :3763-3773
[6]   Minimal sets and chaos in planar piecewise smooth vector fields [J].
Carvalho, Tiago ;
Euzebio, Rodrigo Donizete .
ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2020, (33) :1-15
[7]   Sliding Shilnikov connection in Filippov-type predator-prey model [J].
Carvalho, Tiago ;
Novaes, Douglas Duarte ;
Goncalves, Luiz Fernando .
NONLINEAR DYNAMICS, 2020, 100 (03) :2973-2987
[8]   Teixeira singularities in 3D switched feedback control systems [J].
Colombo, A. ;
di Bernardo, M. ;
Fossas, E. ;
Jeffrey, M. R. .
SYSTEMS & CONTROL LETTERS, 2010, 59 (10) :615-622
[9]   Revisiting the Teixeira Singularity Bifurcation Analysis: Application to the Control of Power Converters [J].
Cristiano, Rony ;
Pagano, Daniel J. ;
Freire, Emilio ;
Ponce, Enrique .
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2018, 28 (09)
[10]   Hopf and Homoclinic bifurcations on the sliding vector field of switching systems in R3: A case study in power electronics [J].
Cristiano, Rony ;
Carvalho, Tiago ;
Tonon, Durval J. ;
Pagano, Daniel J. .
PHYSICA D-NONLINEAR PHENOMENA, 2017, 347 :12-20
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