Globally coupled stochastic two-state oscillators: Fluctuations due to finite numbers

Infinite arrays of coupled two-state stochastic oscillators exhibit well-defined steady states. We study the fluctuations that occur when the number N of oscillators in the array is finite. We choose a particular form of global coupling that in the infinite array leads to a pitchfork bifurcation from a monostable to a bistable steady state, the latter with two equally probable stationary states. The control parameter for this bifurcation is the coupling strength. In finite arrays these states become metastable: The fluctuations lead to distributions around the most probable states, with one maximum in the monostable regime and two maxima in the bistable regime. In the latter regime, the fluctuations lead to transitions between the two peak regions of the distribution. Also, we find that the fluctuations break the symmetry in the bimodal regime, that is, one metastable state becomes more probable than the other, increasingly so with increasing array size. To arrive at these results, we start from microscopic dynamical evolution equations from which we derive a Langevin equation that exhibits an interesting multiplicative noise structure. We also present a master equation description of the dynamics. Both of these equations lead to the same Fokker-Planck equation, the master equation via a 1/N expansion and the Langevin equation via standard methods of Ito calculus for multiplicative noise. From the Fokker-Planck equation we obtain an effective potential that reflects the transition from the monomodal to the bimodal distribution as a function of a control parameter. We present a variety of numerical and analytic results that illustrate the strong effects of the fluctuations. We also show that the limits N -> infinity and t -> infinity(t is the time) do not commute. In fact, the two orders of implementation lead to drastically different results.

Forgotten records of Chrysopelea taprobanica Smith, 1943 (Squamata: Colubridae) from India

The colubrid snake Chrysopelea taprobanica Smith, 1943 was described from a holotype from Kanthali (= Kantalai) and paratypes from Kurunegala, both localities in Sri Lanka (formerly Ceylon) (Smith 1943). Since its description, literature pertaining to Sri Lankan snake fauna considered this taxon to be endemic to the island (Taylor 1950, Deraniyagala 1955, de Silva 1980, de Silva 1990, Somaweera 2004, Somaweera 2006, de Silva 2009, Pyron et al. 2013). In addition, earlier efforts on the Indian peninsula (e.g. Das 1994, 1997, Das 2003, Whitaker & Captain 2004, Aengals et al. 2012) and global data compilations (e.g. Wallach et al. 2014, Uetz & Hošek 2015) did not identify any record from mainland India until Guptha et al. (2015) recorded a specimen (voucher BLT 076 housed at Bio-Lab of Seshachalam Hills, Tirupathi, India) in the dry deciduous forest of Chamala, Seshachalam Biosphere Reserve in Andhra Pradesh, India in November 2013. Guptha et al. (2015) further mentioned an individual previously photographed in 2000 at Rishi Valley, Andhra Pradesh, but with no voucher specimen collected. Guptha’s record, assumed to be the first confirmed record of C. taprobanica in India, is noteworthy as it results in a large range extension, from northern Sri Lanka to eastern India with an Euclidean distance of over 400 km, as well as a change of status, i.e., species not endemic to Sri Lanka. However, at least three little-known previous records of this species from India evaded most literature and were overlooked by the researchers including ourselves.