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In contemporary society, the effective utilization of public resources remains a subject of significant concern. A common issue arises from defectors seeking to obtain an excessive share of these resources for personal gain, potentially…
Competition for a limited resource is the hallmark of many complex systems, and often, that resource turns out to be the physical space itself. In this work, we study a novel model designed to elucidate the dynamics and emergence in complex…
Time delay in general leads to instability in some systems, while a specific feedback with delay can control fluctuated motion in nonlinear deterministic systems to a stable state. In this paper, we consider a non-stationary stochastic…
A simple generative model of a foraging society generates significant wealth inequalities from identical agents on an equal opportunity landscape. These inequalities arise in both equilibrium and non-equilibrium regimes with some societies…
We consider a model of power distribution in a social system where a set of agents play a simple game on a graph: the probability of winning each round is proportional to the agent's current power, and the winner gets more power as a…
Resource are often not uniformly distributed within a population. Spatial variations of concentration of a resource, change the fitness of competing strategies locally. The notion of fitness varying with respect to both genotype and…
Exploiting the mathematical curiosity of intransitive dice, we present a simple theoretical model for co-evolution that captures scales ranging from the genome of the individual to the system-wide emergence of species diversity. We study a…
Kingman's model describes the evolution of a one-locus haploid population of infinite size and discrete generations under the competition of selection and mutation. A random generalisation has been made in a previous paper which assumes all…
For a one-locus haploid infinite population with discrete generations, the celebrated Kingman's model describes the evolution of fitness distributions under the competition of selection and mutation, with a constant mutation probability.…
We replicate a renewal process at random times, which is equivalent to nesting two renewal processes, or considering a renewal process subject to stochastic resetting. We investigate the consequences on the statistical properties of the…
Many complex phenomena, from the selection of traits in biological systems to hierarchy formation in social and economic entities, show signs of competition and heterogeneous performance in the temporal evolution of their components, which…
Natural selection favors the more successful individuals. This is the elementary premise that pervades common models of evolution. Under extreme conditions, however, the process may no longer be probabilistic. Those that meet certain…
The entanglement of population dynamics, evolution, and adaptive radiation for species competing for resources is studied. For resource harvesting, we modify the model used in Ref. Phys. Rev. Lett. 118 048103 and introduce new resource…
Evolving network models under a dynamic growth rule which comprises the addition and deletion of nodes are investigated. By adding a node with a probability $P_a$ or deleting a node with the probability $P_d=1-P_a$ at each time step, where…
In this paper we investigate a structured population model with distributed delay. Our model incorporates two different types of nonlinearities. Specifically we assume that individual growth and mortality are affected by scramble…
The state of many physical, biological and socio-technical systems evolves by combining smooth local transitions and abrupt resetting events to a set of reference values. The inclusion of the resetting mechanism not only provides the…
We investigate the problem of speciation and coexistence in simple ecosystems when the competition among individuals is included in the Eigen model for quasi-species. By suggesting an analogy between the competition among strains and the…
We introduce a non-growth model that generates the power-law distribution with the Zipf exponent. There are N elements, each of which is characterized by a quantity, and at each time step these quantities are redistributed through binary…
Stochastic reaction-diffusion equations are a popular modelling approach for studying interacting populations in a heterogeneous environment under the influence of environmental fluctuations. Although the theoretical basis of alternative…
The occurrence of discrimination is an important problem in the social and economical sciences. Much of the discrimination observed in empirical studies can be explained by the theory of in-group favoritism, which states that people tend to…