Period-halving Bifurcation of a Neuronal Recurrence Equation

Details Period-halving Bifurcation of a Neuronal Recurrence Equation Period-halving Bifurcation of a Neuronal Recurrence Equation

2011-10-17

arxiv.org/abs/1110.3586v3

Computer Science

Neural and Evolutionary Computing

50 pages. This paper was submitted to Complex in July 2010. This paper is the full version of the paper to appear in Volume 20

Scientific paper

We study the sequences generated by neuronal recurrence equations of the form $x(n) = {\bf 1}[\sum_{j=1}^{h} a_{j} x(n-j)- \theta]$. From a neuronal recurrence equation of memory size $h$ which describes a cycle of length $\rho(m) \times lcm(p_0, p_1,..., p_{-1+\rho(m)})$, we construct a set of $\rho(m)$ neuronal recurrence equations whose dynamics describe respectively the transient of length $O(\rho(m) \times lcm(p_0, ..., p_{d}))$ and the cycle of length $O(\rho(m) \times lcm(p_{d+1}, ..., p_{-1+\rho(m)}))$ if $0 \leq d \leq -2+\rho(m)$ and 1 if $d=\rho(m)-1$. This result shows the exponential time of the convergence of neuronal recurrence equation to fixed points and the existence of the period-halving bifurcation.

Affiliated with

Also associated with

No associations

Rating

Period-halving Bifurcation of a Neuronal Recurrence Equation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Period-halving Bifurcation of a Neuronal Recurrence Equation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Period-halving Bifurcation of a Neuronal Recurrence Equation will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-317319