Bayesian ecoevolutionary game dynamics.

The symbiotic relationship between the frameworks of classical game theory and evolutionary game theory is well established. However, evolutionary game theorists have mostly tapped into the classical game of complete information where players are completely informed of all other players' payoffs. Of late, there is a surge of interest in ecoevolutionary interactions where the environment's state is changed by the players' actions which, in turn, are influenced by the changing environment.

Replicator-mutator dynamics of the rock-paper-scissors game: Learning through mistakes.

We generalize the Bush-Mosteller learning, the Roth-Erev learning, and the social learning to include mistakes, such that the nonlinear replicator-mutator equation with either additive or multiplicative mutation is generated in an asymptotic limit. Subsequently, we exhaustively investigate the ubiquitous rock-paper-scissors game for some analytically tractable motifs of mutation pattern for which the replicator-mutator flow is seen to exhibit rich dynamics that include limit cycles and chaotic orbits. The main result of this paper is that in both symmetric and asymmetric game interactions, mistakes can sometimes help the players learn; in fact, mistakes can even control chaos to lead to rational Nash-equilibrium outcomes.

Hypochaos prevents tragedy of the commons in discrete-time eco-evolutionary game dynamics.

While quite a few recent papers have explored game-resource feedback using the framework of evolutionary game theory, almost all the studies are confined to using time-continuous dynamical equations. Moreover, in such literature, the effect of ubiquitous chaos in the resulting eco-evolutionary dynamics is rather missing. Here, we present a deterministic eco-evolutionary discrete-time dynamics in generation-wise non-overlapping population of two types of harvesters-one harvesting at a faster rate than the other-consuming a self-renewing resource capable of showing chaotic dynamics.

Selection-recombination-mutation dynamics: Gradient, limit cycle, and closed invariant curve.

In this paper, the replicator dynamics of the two-locus two-allele system under weak mutation and weak selection is investigated in a generation-wise nonoverlapping unstructured population of individuals mating at random. Our main finding is that the dynamics is gradient-like when the point mutations at the two loci are independent. This is in stark contrast to the case of one-locus-multi-allele where the existence gradient behavior is contingent on a specific relationship between the mutation rates.

Hostility prevents the tragedy of the commons in metapopulation with asymmetric migration: A lesson from queenless ants.

A colony of the queenless ant species, Pristomyrmex punctatus, can broadly be seen as consisting of small-body sized worker ants and relatively larger body-sized cheater ants. Hence, in the presence of intercolony migration, a set of constituent colonies act as a metapopulation exclusively composed of cooperators and defectors. Such a setup facilitates an evolutionary game-theoretic replication-selection model of population dynamics of the ants in a metapopulation.

Periodic orbits in deterministic discrete-time evolutionary game dynamics: An information-theoretic perspective.

Even though the existence of nonconvergent evolution of the states of populations in ecological and evolutionary contexts is an undeniable fact, insightful game-theoretic interpretations of such outcomes are scarce in the literature of evolutionary game theory. As a proof-of-concept, we tap into the information-theoretic concept of relative entropy in order to construct a game-theoretic interpretation for periodic orbits in a wide class of deterministic discrete-time evolutionary game dynamics, primarily investigating the two-player two-strategy case. Effectively, we present a consistent generalization of the evolutionarily stable strategy-the cornerstone of the evolutionary game theory-and aptly term the generalized concept "information stable orbit.

Clinico-demographic profile of COVID-19 positive patients - first wave versus second wave - an experience in north-east India.

Introduction: India witnessed two distinct COVID-19 waves. We evaluated the clinico-demographic profile of patients infected during first wave (FW) and second wave (SW) in a hospital in north-east India.

Methodology: Patients who tested positive for severe acute respiratory syndrome-coronavirus-2 specific gene by reverse transcriptase polymerase chain reaction across FW and SW were diagnosed as COVID-19 positive.

Prevalence, Characteristics, and Correlates of Fatigue in Indian Breast Cancer Survivors: A Cross-Sectional Study.

Navneet Kaur  Fatigue is one of the commonest sequelae of breast cancer treatment that adversely impacts quality of life (QOL) of breast cancer survivors (BCSs). However, very limited data are available about cancer-related fatigue in Indian patients. Hence, this study was planned with the objectives to study (1) prevalence of fatigue in short-, intermediate-, and long-term follow-up; (2) severity and characteristics of fatigue; (3) impact of fatigue on QOL; and (4) correlation of fatigue with other survivorship issues.

Dynamic scaling in rotating turbulence: A shell model study.

We investigate the scaling form of appropriate timescales extracted from time-dependent correlation functions in rotating turbulent flows. In particular, we obtain precise estimates of the dynamic exponents z_{p}, associated with the timescales, and their relation with the more commonly measured equal-time exponents ζ_{p}. These theoretical predictions, obtained by using the multifractal formalism, are validated through extensive numerical simulations of a shell model for such rotating flows.

Game-environment feedback dynamics in growing population: Effect of finite carrying capacity.

The tragedy of the commons (TOC) is an unfortunate situation where a shared resource is exhausted due to uncontrolled exploitation by the selfish individuals of a population. Recently, the paradigmatic replicator equation has been used in conjunction with a phenomenological equation for the state of the shared resource to gain insight into the influence of the games on the TOC. The replicator equation, by construction, models a fixed infinite population undergoing microevolution.

Amplitude death in coupled replicator map lattice: Averting migration dilemma.

Populations composed of a collection of subpopulations (demes) with random migration between them are quite common occurrences. The emergence and sustenance of cooperation in such a population is a highly researched topic in the evolutionary game theory. If the individuals in every deme are considered to be either cooperators or defectors, the migration dilemma can be envisaged: The cooperators would not want to migrate to a defector-rich deme as they fear of facing exploitation; but without migration, cooperation cannot be established throughout the network of demes.

Emergence of universality in the transmission dynamics of COVID-19.

The complexities involved in modelling the transmission dynamics of COVID-19 has been a roadblock in achieving predictability in the spread and containment of the disease. In addition to understanding the modes of transmission, the effectiveness of the mitigation methods also needs to be built into any effective model for making such predictions. We show that such complexities can be circumvented by appealing to scaling principles which lead to the emergence of universality in the transmission dynamics of the disease.

Replicator equations induced by microscopic processes in nonoverlapping population playing bimatrix games.

This paper is concerned with exploring the microscopic basis for the discrete versions of the standard replicator equation and the adjusted replicator equation. To this end, we introduce frequency-dependent selection-as a result of competition fashioned by game-theoretic consideration-into the Wright-Fisher process, a stochastic birth-death process. The process is further considered to be active in a generation-wise nonoverlapping finite population where individuals play a two-strategy bimatrix population game.

Deciphering chaos in evolutionary games.

A discrete-time replicator map is a prototype of evolutionary selection game dynamical models that have been very successful across disciplines in rendering insights into the attainment of the equilibrium outcomes, like the Nash equilibrium and the evolutionarily stable strategy. By construction, only the fixed-point solutions of the dynamics can possibly be interpreted as the aforementioned game-theoretic solution concepts. Although more complex outcomes like chaos are omnipresent in nature, it is not known to which game-theoretic solutions they correspond.

Effect of chaotic agent dynamics on coevolution of cooperation and synchronization.

The effect of chaotic dynamical states of agents on the coevolution of cooperation and synchronization in a structured population of the agents remains unexplored. With a view to gaining insights into this problem, we construct a coupled map lattice of the paradigmatic chaotic logistic map by adopting the Watts-Strogatz network algorithm. The map models the agent's chaotic state dynamics.

Giant Tunable Mechanical Nonlinearity in Graphene-Silicon Nitride Hybrid Resonator.

High quality factor mechanical resonators have shown great promise in the development of classical and quantum technologies. Simultaneously, progress has been made in developing controlled mechanical nonlinearity. Here, we combine these two directions of progress in a single platform consisting of coupled silicon nitride (SiNx) and graphene mechanical resonators.

Evolutionary dynamics of the delayed replicator-mutator equation: Limit cycle and cooperation.

Game theory deals with strategic interactions among players and evolutionary game dynamics tracks the fate of the players' populations under selection. In this paper, we consider the replicator equation for two-player-two-strategy games involving cooperators and defectors. We modify the equation to include the effect of mutation and also delay that corresponds either to the delayed information about the population state or in realizing the effect of interaction among players.

Periodic orbit can be evolutionarily stable: Case Study of discrete replicator dynamics.

In evolutionary game theory, it is customary to be partial to the dynamical models possessing fixed points so that they may be understood as the attainment of evolutionary stability, and hence, Nash equilibrium. Any show of periodic or chaotic solution is many a time perceived as a shortcoming of the corresponding game dynamic because (Nash) equilibrium play is supposed to be robust and persistent behaviour, and any other behaviour in nature is deemed transient. Consequently, there is a lack of attempt to connect the non-fixed point solutions with the game theoretic concepts.

Occasional uncoupling overcomes measure desynchronization.

Owing to the absence of the phase space attractors in the Hamiltonian dynamical systems, the concept of the identical synchronization between the dissipative systems is inapplicable to the Hamiltonian systems for which, thus, one defines a related generalized phenomenon known as the measure synchronization. A coupled pair of Hamiltonian systems-the full coupled system also being Hamiltonian-can possibly be in two types of measure synchronized states: quasiperiodic and chaotic. In this paper, we take representative systems belonging to each such class of the coupled systems and highlight that, as the coupling strengths are varied, there may exist intervals in the ranges of the coupling parameters at which the systems are measure desynchronized.

Finding the Hannay angle in dissipative oscillatory systems via conservative perturbation theory.

Usage of a Hamiltonian perturbation theory for a nonconservative system is counterintuitive and, in general, a technical impossibility by definition. However, the time-independent dual Hamiltonian formalism for the nonconservative systems has opened the door for using various conservative perturbation theories for investigating the dynamics of such systems. Here we demonstrate that the Lie transform Hamiltonian perturbation theory can be adapted to find the perturbative solutions and the frequency corrections for the dissipative oscillatory systems.

Understanding transient uncoupling induced synchronization through modified dynamic coupling.

An important aspect of the recently introduced transient uncoupling scheme is that it induces synchronization for large values of coupling strength at which the coupled chaotic systems resist synchronization when continuously coupled. However, why this is so is an open problem? To answer this question, we recall the conventional wisdom that the eigenvalues of the Jacobian of the transverse dynamics measure whether a trajectory at a phase point is locally contracting or diverging with respect to another nearby trajectory. Subsequently, we go on to highlight a lesser appreciated fact that even when, under the corresponding linearised flow, the nearby trajectory asymptotically diverges away, its distance from the reference trajectory may still be contracting for some intermediate period.

Weight of fitness deviation governs strict physical chaos in replicator dynamics.

Replicator equation-a paradigm equation in evolutionary game dynamics-mathematizes the frequency dependent selection of competing strategies vying to enhance their fitness (quantified by the average payoffs) with respect to the average fitnesses of the evolving population under consideration. In this paper, we deal with two discrete versions of the replicator equation employed to study evolution in a population where any two players' interaction is modelled by a two-strategy symmetric normal-form game. There are twelve distinct classes of such games, each typified by a particular ordinal relationship among the elements of the corresponding payoff matrix.

Interaction Control to Synchronize Non-synchronizable Networks.

Synchronization constitutes one of the most fundamental collective dynamics across networked systems and often underlies their function. Whether a system may synchronize depends on the internal unit dynamics as well as the topology and strength of their interactions. For chaotic units with certain interaction topologies synchronization might be impossible across all interaction strengths, meaning that these networks are non-synchronizable.

Synchronizing noisy nonidentical oscillators by transient uncoupling.

Synchronization is the process of achieving identical dynamics among coupled identical units. If the units are different from each other, their dynamics cannot become identical; yet, after transients, there may emerge a functional relationship between them-a phenomenon termed "generalized synchronization." Here, we show that the concept of transient uncoupling, recently introduced for synchronizing identical units, also supports generalized synchronization among nonidentical chaotic units.