Received 15 May 2011; published 8 August 2011
We investigate the impact of cyclic competition on pattern formation in the rock-paper-scissors game. By separately considering random and prepared initial conditions, we observe a critical influence of the competition rate p on the stability of spiral waves and on the emergence of biodiversity. In particular, while increasing values of p promote biodiversity, they may act detrimentally on spatial pattern formation. For random initial conditions, we observe a phase transition from biodiversity to an absorbing phase, whereby the critical value of mobility grows linearly with increasing values of p on a log-log scale but then saturates as p becomes large. For prepared initial conditions, we observe the formation of single-armed spirals, but only for values of p that are below a critical value. Once above that value, the spirals break up and form disordered spatial structures, mainly because of the percolation of vacant sites. Thus there exists a critical value of the competition rates pc for stable single-armed spirals in finite populations. Importantly though, pc increases with increasing system size because noise reinforces the disintegration of ordered patterns. In addition, we also find that pc increases with the mobility. These phenomena are reproduced by a deterministic model that is based on nonlinear partial differential equations. Our findings indicate that competition is vital for the sustenance of biodiversity and the emergence of pattern formation in ecosystems governed by cyclical interactions.
http://pre.aps.org/abstract/PRE/v84/i2/e026101
Onset of cooperation between layered networks
Received 6 November 2010; revised 11 May 2011; published 3 August 2011
Functionalities of a variety of complex systems involve cooperations among multiple components; for example, a transportation system provides convenient transfers among airlines, railways, roads, and shipping lines. A layered model with interacting networks can facilitate the description and analysis of such systems. In this paper we propose a model of traffic dynamics and reveal a transition at the onset of cooperation between layered networks. The cooperation strength, treated as an order parameter, changes from zero to positive at the transition point. Numerical results on artificial networks as well as two real networks, Chinese and European railway-airline transportation networks, agree well with our analysis.
http://pre.aps.org/abstract/PRE/v84/i2/e026116
Efficient routing strategies in scale-free networks with limited bandwidth
Received 30 April 2010; revised 10 March 2011; published 22 August 2011
We study the traffic dynamics in complex networks where each link is assigned a limited and identical bandwidth. Although the first-in–first-out (FIFO) queuing rule is widely applied in the routing protocol of information packets, here we argue that if we drop this rule, the overall throughput of the network can be remarkably enhanced. We propose some efficient routing strategies that do not strictly obey the FIFO rule. Compared to the routine shortest-path strategy, throughput for both Barabási-Albert (BA) networks and the Internet can be improved by a factor of more than five. We calculate the theoretical limitation of the throughput. In BA networks, our proposed strategy can achieve 88% of the theoretical optimum, yet for the Internet, it is about 12%, implying that we still have a huge space to further improve the routing strategy for the Internet. Finally, we discuss possibly promising ways to design more efficient routing strategies for the Internet.
