Evolutionary games of cyclic competitions have been extensively studied to gain insights into one of the most fundamental phenomena in nature: biodiversity that seems to be excluded by the principle of natural selection. The Rock-Paper-Scissors (RPS) game of three species and its extensions [e.g., the Rock-Paper-Scissors-Lizard-Spock (RPSLS) game] are paradigmatic models in this field. In all previous studies, the intrinsic symmetry associated with cyclic competitions imposes a limitation on the resulting coexistence states, leading to only selective types of such states. We investigate the effect of nonuniform intraspecific competitions on coexistence and find that a wider spectrum of coexistence states can emerge and persist. This surprising finding is substantiated using three classes of cyclic game models through stability analysis, Monte Carlo simulations and continuous spatiotemporal dynamical evolution from partial differential equations. Our finding indicates that intraspecific competitions or alternative symmetry-breaking mechanisms can promote biodiversity to a broader extent than previously thought.

Fins, referred to as extended surfaces, play a crucial role in enhancing heat transfer across various industrial sectors. They achieve this by increasing the surface area available for convective heat transfer. These widespread applications span fields such as energy production, mechanical engineering, surface studies, heat recovery processes, and chemical engineering. The broad utility of fins has prompted researchers to enhance their precision through diverse methods, including numerical, experimental, and analytical approaches. Motivated by these practical applications, this study undertakes a theoretical investigation to analyze the effects of varying fin heights on the behavior of a hybrid hydromagnetic nanofluid within a porous square enclosure. The study explores three distinct cases. In the first case, fixed-height heat fins are attached to the upper and lower walls. In the second case, the fin attached to the upper wall remains static, while those on the lower wall are extended from 0.25L to 0.5L. Conversely, the third case involves extending the height of the upper fin from 0.25L to 0.5L. The in-house MATLAB code, coupled with a finite difference method, is employed to solve the governing equations, and its reliability is confirmed through comparison with prior publications. Thorough numerical simulations are conducted, encompassing control parameters such as thermal radiation, Rayleigh number, nanoparticle volume fraction, Hartmann number, heat generation/absorption, and Darcy number. The numerical results are visually presented through streamlines, isotherms, and average Nusselt number plots, elucidating the impact of these parameters across a range of scenarios. It is noticed that case 3 exposes a 96.06% higher heat transfer rate than case 2 with higher values of volume fraction and Rayleigh number. In all three cases, the Rayleigh number and Hartmann number cause a reduction in the entropy generation. For a higher Rayleigh number, employing a hybrid nanofluid containing a volume fraction of 5% causes a 110.41% reduction in heat transfer for the case involving bottom fin height compared to case 1. Similarly, extending the top fin leads to a heat transfer reduction of 100.41%.

Alternative strategy is common in animal populations to promote reproductive fitness by obtaining resources. In spatial dynamics of cyclic competition, reproduction can occur when individuals obtain vacant rooms and, in this regard, empty sites should be resources for reproduction which can be induced by interspecific competition. In this paper, we study the role of alternative competition in the spatial system of cyclically competing five species by utilizing rock-paper-scissors-lizard-spock game. From Monte-Carlo simulations, we found that strong alternative competition can lead to the reemergence of coexistence of five species regardless of mobility, which is never reported in previous works under the symmetric competition structure. By investigating the coexistence probability, we also found that coexistence alternates by passing certain degrees of alternative competition in combination with mobility. In addition, we provided evidences in the opposite scenario by strengthening spontaneous competition, which exhibits the reemergence of coexistence similarly. Our findings may suggest more comprehensive perspectives to interpret mechanisms for biodiversity by alternative strategies in spatially extended systems than previously reported.