No abstract

Rumor spreading can have a significant impact on people’s lives, distorting scientific facts and influencing political opinions. With technologies that have democratized the production and reproduction of information, the rate at which misinformation can spread has increased significantly, leading many to describe contemporary times as a ‘post-truth era’. Research into rumor spreading has primarily been based on either model of social and biological contagion, or upon models of opinion dynamics. Here we present a comprehensive model that is based on information entropy, which allows for the incorporation of considerations like the role of memory, conformity effects, differences in the subjective propensity to produce distortions, and variations in the degree of trust that people place in each other. Variations in the degree of trust are controlled by a confidence factor β, while the propensity to produce distortions is controlled by a conservation factor K. Simulations were performed using a Barabási–Albert (BA) scale-free network seeded with a single piece of information. The influence of β and K upon the temporal evolution of the system was subsequently analyzed regarding average information entropy, opinion fragmentation, and the range of rumor spread. These results can aid in decision-making to limit the spread of rumors.

No abstract

Organisms with environmental sensors that guide survival are considered more likely to be favored by natural selection if they possess more accurate sensors. In this paper, we develop a theoretical model which shows that under certain conditions of environmental stochasticity, selection actually favors sensors of lower accuracy. An analogy between this counter-intuitive phenomenon and the well-known Parrondo’s paradox is suggested.

Parrondo’s games were first constructed using a simple tossing scenario, which demonstrates the following paradoxical situation: in sequences of games, a winning expectation may be obtained by playing the games in a random order, although each game (game A or game B) in the sequence may result in losing when played individually. The available Parrondo’s games based on the spatial niche (the neighboring environment) are applied in the regular networks. The neighbors of each node are the same in the regular graphs, whereas they are different in the complex networks. Here, Parrondo’s model based on complex networks is proposed, and a structure of game B applied in arbitrary topologies is constructed. The results confirm that Parrondo’s paradox occurs. Moreover, the size of the region of the parameter space that elicits Parrondo’s paradox depends on the heterogeneity of the degree distributions of the networks. The higher heterogeneity yields a larger region of the parameter space where the strong paradox occurs. In addition, we use scale-free networks to show that the network size has no significant influence on the region of the parameter space where the strong or weak Parrondo’s paradox occurs. The region of the parameter space where the strong Parrondo’s paradox occurs reduces slightly when the average degree of the network increases.

Previously, we developed a population model incorporating the Allee effect and periodic environmental fluctuations, in which organisms alternate between nomadic and colonial behaviours. This switching strategy is regulated by biological clocks and the abundance of environmental resources, and can lead to population persistence despite both behaviours being individually losing. In the present study, we consider stochastic noise models in place of the original periodic ones, thereby allowing a wider range of environmental fluctuations to be modelled. The theoretical framework is generalized to account for resource depletion by both nomadic and colonial sub-populations, and an ecologically realistic population size-dependent switching scheme is proposed. We demonstrate the robustness of the modified switching scheme to stochastic noise, and we also present the intriguing possibility of consecutive subsidence-recovery cycles within the resulting population dynamics. Our results have relevance in biological and physical systems.

No abstract

In this paper, a state constraint controller with disturbance compensation is proposed for uncertain nonlinear systems to improve the control performance without violating the full state constraints. A series of extended state observers are designed to estimate disturbances that include the unmodeled dynamics and the modeling errors. To guarantee non-violation of state constraints while compensating the disturbances, based on the backstepping technique, the state constraint controller with extended state observer is proposed by using the barrier Lyapunov function. Then, the stability of the closed-loop system is proved theoretically. Moreover, exponentially asymptotic tracking is achieved when the disturbances are not time-variant. Finally, the effectiveness of the proposed approach is verified by two examples.