Data analytic study of the homothermal maintenance mechanism of Skunk Cabbage: Capturing pre-equilibrium characteristics using extended poisson model

A wild plant called Skunk Cabbage is known to heat itself and keep its body warm before spring. We study its homothermal maintenance mechanism from a mesoscopic point of view. We take the increment process of the temperature time series and consider it as ‘elastic’ force that always tries to backlash its temperature to an intrinsic target temperature. We then propose a kind of extended Poisson distribution for the model of the ‘elastic’ force. The hypothesis testing result by Kolmogorov-Smirnov test suggests that the proposed distribution is a plausible candidate of the model for the ‘elastic’ force, on the temperature range in which the system is in equillibrium. In addition, it turns out that the parameters in the model captures well the linear behaviour of the expectations of the ‘elastic’ force at each of the present temperatures and similarly, the constancy of the variances of the force. Especially, the linearity of the expected increments over displacements of tempertures indicates that the backlash might be considered to be like the elastic force of a spring as described by Fuch’s law.