Nonlinear Dynamics and Chaos of the Daisyworld Employed for Global Warming Description

Abstract

Abstract. The mathematical modeling of ecological phenomena may describe time evolution and spatial distribution being capable to explain some important characteristics of ecological systems. Although there are many difficulties related to the system description, their modeling may define at least a system caricature, which may be useful for different goals. This contribution deals with the modeling of the global warming in a nonlinear dynamics point of view. Mathematical modeling is based on the daisyworld that is able to describe the global regulation that can emerge from the interaction between life and environment. In brief, daisyworld represents life by daisy populations while the environment is represented by temperature. Here, two daisy populations are of concern, black and white daisies, and an extra variable related to greenhouse gases is incorporated in the model allowing the analysis of the global warming. Moreover, transient analysis of temperature evolution is of concern. Climate variability is represented by a sinusoidal variation of the luminosity. Numerical simulations are investigated in order to present a qualitative description of the phenomenon. Daisyworld dynamics presents a rich behavior including chaos.

Toy models for macroevolutionary patterns and trends

“…Higher dimensional versions add one dimension (latitude) (Biton and Gildor, 2012) or use cellular automata or networks to let the daisies spread in two dimensions (Punithan et al, 2011(Punithan et al, , 2012. Recent additions to modeling include symbiosis (Boyle et al, 2011), greenhouse gases (Viola et al, 2013), and time scale analysis (Weaver and Dyke, 2012). A Daisyworld approach to Fig.…”

Dynamical behavior analysis of the Van der Pol oscillator with sine nonlinearity subjected to non-sinusoidal periodic excitations by the bifurcation structures

“…These non-linear oscillators include the FitzHugh and Nagumo oscillato [11], the Hodgkin-Huxley oscillator [12], the Grudzinski-Zebrowski oscillator [13], the Hartley model [14], the Colpitts model [15], the Tchitnga oscillator [16], etc The results obtained thanks to the richness of their dynamics have contributed to major advances in many areas of research, both fundamental and engineering. [8,[17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32].…”

Plant-microbe symbiosis widens the habitability range of the Daisyworld

“…The Daisyworld model has been studied and modified in multiple ways in an attempt to reduce the simplifications and to understand the conditions for regulation (Lenton et al, 2020). These modifications include extensions to one dimension (Adams et al, 2003;Biton and Gildor, 2012;Alberti et al, 2015) and two spatial dimensions (Von Bloh et al, 1999;Punithan et al, 2012;Punithan and McKay, 2014;Kageyama and Yagi, 2020), the effect of greenhouse gases (Maddock, 1991;Nordstrom et al, 2005;Viola et al, 2013;Paiva et al, 2014;Alberti et al, 2015;Rueangphankun et al, 2018), multiple species and trophic levels (Keeling, 1991;Lovelock, 1992;Lenton and Lovelock, 2001), the role of the hydrological cycle (precipitation, evapotranspiration, clouds, etc.) (Nordstrom et al, 2005;Salazar and Poveda, 2009), mutation (Robertson and Robinson, 1998), destructive environmental feedbacks (Watson and Lovelock, 1983), discretisation of the albedo trait space (Lovelock, 1992), physical constraints on adaptation (Lenton and Lovelock, 2000), time scales perspective (Weaver and Dyke, 2012), and habitat fragmentation (Von Bloh et al, 1999).…”