On the Stabilizing Effect of Predators and Competitors on Ecological Communities

Ecological communities can lose their permanence if a predator or a competitor is removed: the remaining species no linger coexist. This well known phenomenon is analyzed for some low dimensional examples of Lotka-Volterra type, with special attention paid to the occurrence of heteroclinic cycles

Heteroclinic Chaos, Chaotic Itinerancy and Neutral Attractors in Symmetrical Replicator Equations with Mutations

A replicator equation with mutation processes is numerically studied. Without any mutations, two characteristics of the replicator dynamics are known: an exponential divergence of the dominance period, and hierarchical orderings of the attractors. A mutation introduces some new aspects: the emergence of structurally stable attractors, and chaotic itinerant behavior. In addition, it is reported that a neutral attractor can exist in the mutataion rate -> +0 region.Comment: 4 pages, 9 figure

Dynamically generated cyclic dominance in spatial prisoner's dilemma games

We have studied the impact of time-dependent learning capacities of players in the framework of spatial prisoner's dilemma game. In our model, this capacity of players may decrease or increase in time after strategy adoption according to a step-like function. We investigated both possibilities separately and observed significantly different mechanisms that form the stationary pattern of the system. The time decreasing learning activity helps cooperator domains to recover the possible intrude of defectors hence supports cooperation. In the other case the temporary restrained learning activity generates a cyclic dominance between defector and cooperator strategies, which helps to maintain the diversity of strategies via propagating waves. The results are robust and remain valid by changing payoff values, interaction graphs or functions characterizing time-dependence of learning activity. Our observations suggest that dynamically generated mechanisms may offer alternative ways to keep cooperators alive even at very larger temptation to defect.Comment: 7 pages, 6 figures, accepted for publication in Physical Review

Segregation process and phase transition in cyclic predator-prey models with even number of species

We study a spatial cyclic predator-prey model with an even number of species (for n=4, 6, and 8) that allows the formation of two defective alliances consisting of the even and odd label species. The species are distributed on the sites of a square lattice. The evolution of spatial distribution is governed by iteration of two elementary processes on neighboring sites chosen randomly: if the sites are occupied by a predator-prey pair then the predator invades the prey's site; otherwise the species exchange their site with a probability $X$. For low $X$ values a self-organizing pattern is maintained by cyclic invasions. If $X$ exceeds a threshold value then two types of domains grow up that formed by the odd and even label species, respectively. Monte Carlo simulations indicate the blocking of this segregation process within a range of X for n=8.Comment: 5 pages, 5 figures, to be appear in Phys. Rev.

The Dynamics of Asymmetric Games

A game dynamical analysis of a simple asymmetric game (two roles with two alternatives each) shows that an interesting class of "semi-stable" heteroclinic cycles leading to a highly unpredictable behavior can occur in a robust way. Biological examples related to conflicts over ownership and parental investment are analyzed

Design Requirements for Pressurized Chemical Looping Reforming

A key issue in chemical looping reforming is to operate the process under pressurized conditions. Applicability of dual fluidized bed systems, currently used in atmospheric chemical looping processes, is affected by pressure. Critical design issues were studied and experimentally verified by cold flow model experiments. It turns out that it is important to achieve sufficient global solids circulation and to keep the pressure difference between the reactors low enough for proper operation of the loop seals

Oscillations in Optional Public Good Games

We present a new mechanism promoting cooperative behavior among selfish individuals in the public goods game. This game represents a straightforward generalization of the prisoner's dilemma to an arbitrary number of players. In contrast to the compulsory public goods game, optional participation provides a natural way to avoid deadlocks in the state of mutual defection. The three resulting strategies - collaboration or defection in the public goods game, as well as not joining at all -are studied by means of a replicator dynamics, which can be completely analysed in spite of the fact that some payoff terms are nonlinear. If cooperation is valuable enough, the dynamics exhibits a rock-scissors-paper type of cycling between the three strategies, leading to sizeable average levels of cooperation in the population. Thus, voluntary participation makes cooperation possible. But for each strategy, the average payoff value remains equal to the earnings of those not participating in the public goods game

State Differentiation by Transient Truncation in Coupled Threshold Dynamics

Dynamics with a threshold input--output relation commonly exist in gene, signal-transduction, and neural networks. Coupled dynamical systems of such threshold elements are investigated, in an effort to find differentiation of elements induced by the interaction. Through global diffusive coupling, novel states are found to be generated that are not the original attractor of single-element threshold dynamics, but are sustained through the interaction with the elements located at the original attractor. This stabilization of the novel state(s) is not related to symmetry breaking, but is explained as the truncation of transient trajectories to the original attractor due to the coupling. Single-element dynamics with winding transient trajectories located at a low-dimensional manifold and having turning points are shown to be essential to the generation of such novel state(s) in a coupled system. Universality of this mechanism for the novel state generation and its relevance to biological cell differentiation are briefly discussed.Comment: 8 pages. Phys. Rev. E. in pres

Correlation of Positive and Negative Reciprocity Fails to Confer an Evolutionary Advantage: Phase Transitions to Elementary Strategies

Economic experiments reveal that humans value cooperation and fairness. Punishing unfair behavior is therefore common, and according to the theory of strong reciprocity, it is also directly related to rewarding cooperative behavior. However, empirical data fail to confirm that positive and negative reciprocity are correlated. Inspired by this disagreement, we determine whether the combined application of reward and punishment is evolutionarily advantageous. We study a spatial public goods game, where in addition to the three elementary strategies of defection, rewarding, and punishment, a fourth strategy that combines the latter two competes for space. We find rich dynamical behavior that gives rise to intricate phase diagrams where continuous and discontinuous phase transitions occur in succession. Indirect territorial competition, spontaneous emergence of cyclic dominance, as well as divergent fluctuations of oscillations that terminate in an absorbing phase are observed. Yet, despite the high complexity of solutions, the combined strategy can survive only in very narrow and unrealistic parameter regions. Elementary strategies, either in pure or mixed phases, are much more common and likely to prevail. Our results highlight the importance of patterns and structure in human cooperation, which should be considered in future experiments