Open AccessStability and neimark - sacker bifurcation for a discrete system of one - scroll chaotic attractor with fractional order
Author(s) -
A. George Maria Selvam,
R. Dhineshbabu,
Özlem Ak Gümüş
Publication year - 2020
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1597/1/012009
Subject(s) - attractor , mathematics , bifurcation , bifurcation diagram , discretization , chaotic , parametric statistics , biological applications of bifurcation theory , stability (learning theory) , saddle node bifurcation , statistical physics , mathematical analysis , control theory (sociology) , nonlinear system , computer science , physics , statistics , quantum mechanics , artificial intelligence , machine learning , control (management)
This present work investigates the dynamical behaviors of a new form of fractional order three dimensional system with a chaotic attractor of the one-scroll structure and its discretized counterpart. Firstly, existence and parametric conditions for local stability analysis of steady states of the model are addressed. Then the bifurcation theory is applied to investigate the presence of Neimark - Sacker (NS) bifurcations at the coexistence steady state taking the time delay as a bifurcation parameter in the discrete fractional order system. Also the trajectories, phase diagrams, limit cycles, bifurcation diagrams, attractors for period - 1, 2, 3, 4, 5 and a chaotic attractor with one scroll are exhibited for biologically meaningful sets of parameter values in the discretized system. Finally, several numerical examples are presented to assure the validity of the theoretical results and further rich dynamics of the model is explored as well.