TY - JOUR
T1 - Linearizability conditions for Lotka-Volterra planar complex quartic systems having homogeneous nonlinearities
AU - Giné, Jaume
AU - Kadyrsizova, Zhibek
AU - Liu, Yirong
AU - Romanovski, Valery G.
N1 - Funding Information:
The authors are grateful to the referees for their valuable remarks which helped to improve the manuscript. The first author is partially supported by a MCYT/FEDER grant number MTM2008-00694 and by a CIRIT grant number 2009SGR 381 . The third author is partially supported by the National Natural Science Foundation of China ( 10771196 ). The fourth author is supported by the Slovenian Research Agency , by the Nova Kreditna Banka Maribor , by TELEKOM Slovenije , and by the Transnational Access Programme at RISC-Linz of the European Commission Framework 6 Programme for Integrated Infrastructures Initiatives under the project SCIEnce (Contract No. 026133 ).
PY - 2011/2
Y1 - 2011/2
N2 - In this paper we investigate the linearizability problem for the two-dimensional Lotka-Volterra complex quartic systems which are linear systems perturbed by fourth degree homogeneous polynomials, i.e., we consider systems of the form x=x(1-a30x3-a21x2y-a 12xy2-a03y3), y=-y(1-b 30x3-b21x2y-b12xy 2-b03y3). The necessary and sufficient conditions for the linearizability of this system are found. From them the conditions for isochronicity of the corresponding real system can be derived.
AB - In this paper we investigate the linearizability problem for the two-dimensional Lotka-Volterra complex quartic systems which are linear systems perturbed by fourth degree homogeneous polynomials, i.e., we consider systems of the form x=x(1-a30x3-a21x2y-a 12xy2-a03y3), y=-y(1-b 30x3-b21x2y-b12xy 2-b03y3). The necessary and sufficient conditions for the linearizability of this system are found. From them the conditions for isochronicity of the corresponding real system can be derived.
KW - Isochronicity
KW - Linearizability
KW - Polynomial differential system
KW - Polynomial vector field
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U2 - 10.1016/j.camwa.2010.12.069
DO - 10.1016/j.camwa.2010.12.069
M3 - Article
AN - SCOPUS:79651469384
VL - 61
SP - 1190
EP - 1201
JO - Computers and Mathematics with Applications
JF - Computers and Mathematics with Applications
SN - 0898-1221
IS - 4
ER -