Journal
NONLINEAR DYNAMICS
Volume 70, Issue 3, Pages 1719-1730Publisher
SPRINGER
DOI: 10.1007/s11071-012-0568-y
Keywords
Chaos; Spiral wave; Excitable system; Arnold tongue
Categories
Funding
- National Natural Science Foundation of China [11005030, 11075021]
- Science Foundations of Hebei Education Department [2009135]
- Hebei Nature Science Foundation Project [A2006000128]
- Science Foundation Of Hebei Normal University
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We study the effects of a dichotomous periodic force on meandering and rigidly rotating spiral waves. For a meandering state, the periodic forcing induces more modulating frequencies according to the rules of frequency-locked relations and linear combinations. It can also generate some unique closed tip orbits. On the modulating period T-axis, there exist all kinds of resonant entrainment bands. Arnold tongues exist in the period-amplitude space. The width of entrainment bands is affected by the symmetry of positive and negative parts in each signal unit. In addition, appropriate choices of T-value can be used to eliminate spiral waves. For a rigidly rotating state, the periodic forcing can induce a transition toward meandering spiral waves via generating a transitive bidirectional spiral wave. It is very interesting that, after the transition, the meandering spiral wave has the same primary rotating period as the free meandering states.
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