Rulkov Map in the Superior Orbit
Rulkov map is two dimensional map that replicates the dynamics of spiking-bursting and spiking activity of real biological neuron. It contains one fast and one slow variable. In this paper, we have studied rulkov map in superior orbit and we have shown that the behavior of neuron for α > 4 is spiking-busting whereas earlier in picard orbit its behavior is chaotic. A few examples have been studied by applying superior orbit to the rulkov map.
KeywordsRulkov map Picard orbit Superior orbit
- 2.Rulkov NF (2002) Modeling of spiking-bursting neural behavior using two dimensional map. Physical Rev Lett 65:041922(1–9)Google Scholar
- 5.Rani M (2002) Iterative procedure in fractals and chaos. Dissertation, Gurukala Kangri Vishwavidyalaya, Hardwar, IndiaGoogle Scholar
- 9.Rani M, Agarwal R (2009) A new experimental approach to study the stability of logistic map. Chaos Soliton Fract 41(4):2062–2066Google Scholar
- 10.Rani M, Kumar V (2005) A new experiment with the logistic map. J Indian Acad Math 27(1):143–156 (MR2224669)Google Scholar
- 11.Mann WR (1953) Mean value methods in iteration. P Am Math Soc 4:506–510 (MR54846)Google Scholar