000307722 001 __ 307722
000307722 005 __ 20250210092747.0
000307722 024 7_ $2 doi $a 10.1016/j.chaos.2024.115768
000307722 024 8_ $9 scholar $9 driver $9 artpubuab $a oai:ddd.uab.cat:307722
000307722 035 __ $9 scopus_id $a 85210065552
000307722 035 __ $9 articleid $a 09600779v190p115768
000307722 035 __ $9 gsduab $a 6074
000307722 035 __ $a oai:egreta.uab.cat:publications/87594bb1-0cdb-46ae-acb1-c25ad0cc5a88
000307722 041 __ $a eng
000307722 100 1_ $0 0000-0003-1400-4136 $a Ginoux, Jean-Marc $u Istituto Nazionale di Ottica
000307722 245 10 $a Energy function of 2D and 3D dynamical systems
000307722 251 __ $1 http://purl.org/coar/version/c_ab4af688f83e57aa $2 openaire4 $9 AM $a Versió acceptada per publicar
000307722 260 __ $c 2025
000307722 520 3_ $a It is far well-known that energy function of a two-dimensional autonomous dynamical system can be simply obtained by multiplying its corresponding second-order ordinary differential equation, i.e., its equation of motion by the first time derivative of its state variable. In the nineties, one of us (J.C.S.) stated that a three-dimensional autonomous dynamical system can be also transformed into a third-order ordinary differential equation of motion todays known as jerk equation. Although a method has been developed during these last decades to provide the energy function of such three-dimensional autonomous dynamical systems, the question arose to determine by which type of term, i.e., by the first or second time derivative of their state variable, the corresponding jerk equation of these systems should be multiplied to deduce their energy function. We prove in this work that the jerk equation of such systems must be multiplied by the second time derivative of the state variable and not by the first like in dimension two. We then provide an interpretation of the new term appearing in the energy function and called jerk energy. We thus established that it is possible to obtain the energy function of a three-dimensional dynamical system directly from its corresponding jerk equation. Two and three-dimensional Van der Pol models are then used to exemplify these main results. Applications to Lorenz and Chua's models confirms their validity.
000307722 536 __ $a Agencia Estatal de Investigación $d https://doi.org/10.13039/501100011033 $f PID2022-136613NB-I00
000307722 536 __ $a Agència de Gestió d'Ajuts Universitaris i de Recerca $d https://doi.org/10.13039/501100003030 $f 2021/SGR-00113
000307722 540 __ $9 embargoed access $a Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades. $u https://creativecommons.org/licenses/by-nc-nd/4.0/
000307722 546 __ $a Anglès
000307722 599 __ $a recerca
000307722 655 _7 $1 http://purl.org/coar/resource_type/c_6501 $2 openaire4 $a Article $c literature
000307722 700 1_ $a Meucci, Riccardo $u Istituto Nazionale di Ottica
000307722 700 1_ $0 0000-0002-9511-5999 $a Llibre, Jaume $u Universitat Autònoma de Barcelona. Departament de Matemàtiques
000307722 700 1_ $0 0000-0001-7014-3283 $a Sprott, Julien Clinton $u University of Wisconsin
000307722 773 __ $g Vol. 190 (January 2025), art. 115768 $t Chaos, solitons and fractals $x 0960-0779
000307722 856 42 $u https://ddd.uab.cat/img/uab/embargament.png $v info:eu-repo/date/embargoEnd/2027-01-31 $z Postprint
000307722 973 __ $f 115768 $m 1 $v 190 $x 0960-0779_a2025m1v190n $y 2025
000307722 980 __ $a ARTPUB $b UAB $b GSDUAB