TY - JOUR
T1 - On the n-dimensional phase portraits
AU - Rodríguez-Licea, Martín Antonio
AU - Perez-Pinal, Francisco J.
AU - Nuñez-Pérez, José Cruz
AU - Sandoval-Ibarra, Yuma
N1 - Publisher Copyright:
© 2019 by the authors.
PY - 2019
Y1 - 2019
N2 - The phase portrait for dynamic systems is a tool used to graphically determine the instantaneous behavior of its trajectories for a set of initial conditions. Classic phase portraits are limited to two dimensions and occasionally snapshots of 3D phase portraits are presented; unfortunately, a single point of view of a third or higher order system usually implies information losses. To solve that limitation, some authors used an additional degree of freedom to represent phase portraits in three dimensions, for example color graphics. Other authors perform states combinations, empirically, to represent higher dimensions, but the question remains whether it is possible to extend the two-dimensional phase portraits to higher order and their mathematical basis. In this paper, it is reported that the combinations of states to generate a set of phase portraits is enough to determine without loss of information the complete behavior of the immediate system dynamics for a set of initial conditions in an n-dimensional state space. Further, new graphical tools are provided capable to represent methodically the phase portrait for higher order systems.
AB - The phase portrait for dynamic systems is a tool used to graphically determine the instantaneous behavior of its trajectories for a set of initial conditions. Classic phase portraits are limited to two dimensions and occasionally snapshots of 3D phase portraits are presented; unfortunately, a single point of view of a third or higher order system usually implies information losses. To solve that limitation, some authors used an additional degree of freedom to represent phase portraits in three dimensions, for example color graphics. Other authors perform states combinations, empirically, to represent higher dimensions, but the question remains whether it is possible to extend the two-dimensional phase portraits to higher order and their mathematical basis. In this paper, it is reported that the combinations of states to generate a set of phase portraits is enough to determine without loss of information the complete behavior of the immediate system dynamics for a set of initial conditions in an n-dimensional state space. Further, new graphical tools are provided capable to represent methodically the phase portrait for higher order systems.
KW - High order system
KW - N-dimensional
KW - Phase portrait
UR - http://www.scopus.com/inward/record.url?scp=85063751626&partnerID=8YFLogxK
U2 - 10.3390/app9050872
DO - 10.3390/app9050872
M3 - Artículo
AN - SCOPUS:85063751626
SN - 2076-3417
VL - 9
JO - Applied Sciences (Switzerland)
JF - Applied Sciences (Switzerland)
IS - 5
M1 - 872
ER -