Comparing the influence of distinct kinds of temporal disorder in a low-dimensional absorbing transition model

Influence of distinct kinds of temporal disorder in discontinuous phase transitions

Based on mean-field theory (MFT) arguments, a general description for discontinuous phase transitions in the presence of temporal disorder is considered. Our analysis extends the recent findings [C. E. Fiore et al., Phys. Rev. E 98, 032129 (2018)2470-004510.1103/PhysRevE.98.032129] by considering discontinuous phase transitions beyond those with a single absorbing state. The theory is exemplified in one of the simplest (nonequilibrium) order-disorder (discontinuous) phase transitions with "up-down" Z_{2} symmetry: the inertial majority vote model for two kinds of temporal disorder. As for absorbing phase transitions, the temporal disorder does not suppress the occurrence of discontinuous phase transitions, but remarkable differences emerge when compared with the pure (disorderless) case. A comparison between the distinct kinds of temporal disorder is also performed beyond the MFT for random-regular complex topologies. Our work paves the way for the study of a generic discontinuous phase transition under the influence of an arbitrary kind of temporal disorder.

The advantage of being slow: The quasi-neutral contact process

According to the competitive exclusion principle, in a finite ecosystem, extinction occurs naturally when two or more species compete for the same resources. An important question that arises is: when coexistence is not possible, which mechanisms confer an advantage to a given species against the other(s)? In general, it is expected that the species with the higher reproductive/death ratio will win the competition, but other mechanisms, such as asymmetry in interspecific competition or unequal diffusion rates, have been found to change this scenario dramatically. In this work, we examine competitive advantage in the context of quasi-neutral population models, including stochastic models with spatial structure as well as macroscopic (mean-field) descriptions. We employ a two-species contact process in which the “biological clock” of one species is a factor of αslower than that of the other species. Our results provide new insights into how stochasticity and competition interact to determine extinction in finite spatial systems. We find that a species with a slower biological clock has an advantage if resources are limited, winning the competition against a species with a faster clock, in relatively small systems. Periodic or stochastic environmental variations also favor the slower species, even in much larger systems.

Temporal disorder does not forbid discontinuous absorbing phase transitions in low-dimensional systems

Recent papers have shown that spatial (quenched) disorder can suppress discontinuous absorbing phase transitions. Conversely, the scenario for temporal disorder is still unknown. To shed some light in this direction, we investigate its effect in three different two-dimensional models which are known to exhibit discontinuous absorbing phase transitions. The temporal disorder is introduced by allowing the control parameter to be time dependent p→p(t), either varying as a uniform distribution with mean p[over ¯] and variance σ or as a bimodal distribution, fluctuating between a value p and a value p_{l}≪p. In contrast to spatial disorder, our numerical results strongly suggest that such uncorrelated temporal disorder does not forbid the existence of a discontinuous absorbing phase transition. We find that all cases are characterized by behaviors similar to their pure (without disorder) counterparts, including bistability around the coexistence point and common finite-size scaling behavior with the inverse of the system volume, as recently proposed [M. M. de Oliveira et al., Phys. Rev. E 92, 062126 (2015)PLEEE81539-375510.1103/PhysRevE.92.062126]. We also observe that temporal disorder does not induce temporal Griffiths phases around discontinuous phase transitions, at least not for d=2.