The universality class of random searches in critically scarce environments

¹ Departamento de Física, Universidade Federal do Paraná - 81531-980, Curitiba-PR, Brazil
² Campus Arapiraca, Universidade Federal de Alagoas - 57309-005, Arapiraca-AL, Brazil
³ Instituto de Física, Universidade Federal de Alagoas - 57072-970, Maceió-AL, Brazil
⁴ Laboratório de Física Teórica e Computacional, Departamento de Física, Universidade Federal de Pernambuco 50670-901, Recife-PE, Brazil
⁵ Departamento de Física Teórica e Experimental, Universidade Federal do Rio Grande do Norte 59078-900, Natal-RN, Brazil

^a luz@fisica.ufpr.br

Received: 11 October 2011
Accepted: 26 January 2012

Abstract

We analyze searchers looking for diffusive targets when the formers rely on the net energy gained from the encounters to maintain the process. The system properties are studied at very low target densities, for the searchers at the edge of extinction. We report that superdiffusion for both types of players confers a substantial increase in the searchers survival rate. A continuous phase transition is observed for any search strategy. From the critical exponents, we find that the problem belongs to the same universality class of directed percolation with absorbing walls. We finally discuss the implications of the random search process criticality to the endurance of searchers as a group and eventual connections with the preservation of biological species.