TY - GEN
T1 - Frequency-input-timescale relations in two-dimensional Hindmarsh-Rose model
AU - Sato, Yasuomi D.
PY - 2012/12/1
Y1 - 2012/12/1
N2 - Stability analysis and control of two-timescale systems are of importance for understanding oscillation emergence mechanisms. In this work, we study theoretically frequency-input-timescale (called the f-z-μ) relation in the two-dimensional Hindmarsh-Rose (2DHR) oscillator. All bifurcations of saddle-node, Andronov-Hopf and saddle-node on invariant cycle are also computed with the respective parameter sets, giving the respective frequency gradient equation in terms of z and μ derived by approaches of their small perturbation on the oscillation. The core target in this analysis is to understand dynamical property of the f-μ cleft on the 2DHR undergoing the SNIC bifurcation, compared to oscillatory dynamics of the system exhibiting the other bifurcations.
AB - Stability analysis and control of two-timescale systems are of importance for understanding oscillation emergence mechanisms. In this work, we study theoretically frequency-input-timescale (called the f-z-μ) relation in the two-dimensional Hindmarsh-Rose (2DHR) oscillator. All bifurcations of saddle-node, Andronov-Hopf and saddle-node on invariant cycle are also computed with the respective parameter sets, giving the respective frequency gradient equation in terms of z and μ derived by approaches of their small perturbation on the oscillation. The core target in this analysis is to understand dynamical property of the f-μ cleft on the 2DHR undergoing the SNIC bifurcation, compared to oscillatory dynamics of the system exhibiting the other bifurcations.
UR - http://www.scopus.com/inward/record.url?scp=84877800440&partnerID=8YFLogxK
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U2 - 10.1109/SCIS-ISIS.2012.6505138
DO - 10.1109/SCIS-ISIS.2012.6505138
M3 - Conference contribution
AN - SCOPUS:84877800440
SN - 9781467327428
T3 - 6th International Conference on Soft Computing and Intelligent Systems, and 13th International Symposium on Advanced Intelligence Systems, SCIS/ISIS 2012
SP - 315
EP - 320
BT - 6th International Conference on Soft Computing and Intelligent Systems, and 13th International Symposium on Advanced Intelligence Systems, SCIS/ISIS 2012
T2 - 2012 Joint 6th International Conference on Soft Computing and Intelligent Systems, SCIS 2012 and 13th International Symposium on Advanced Intelligence Systems, ISIS 2012
Y2 - 20 November 2012 through 24 November 2012
ER -