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

Recurrence spectrum in smooth dynamical systems

We prove that for conformal expanding maps the return time does have constant multifractal spectrum. This is the counterpart of the result by Feng and Wu in the symbolic setting

Resonance bifurcations from robust homoclinic cycles

We present two calculations for a class of robust homoclinic cycles with symmetry Z_n x Z_2^n, for which the sufficient conditions for asymptotic stability given by Krupa and Melbourne are not optimal. Firstly, we compute optimal conditions for asymptotic stability using transition matrix techniques which make explicit use of the geometry of the group action. Secondly, through an explicit computation of the global parts of the Poincare map near the cycle we show that, generically, the resonance bifurcations from the cycles are supercritical: a unique branch of asymptotically stable period orbits emerges from the resonance bifurcation and exists for coefficient values where the cycle has lost stability. This calculation is the first to explicitly compute the criticality of a resonance bifurcation, and answers a conjecture of Field and Swift in a particular limiting case. Moreover, we are able to obtain an asymptotically-correct analytic expression for the period of the bifurcating orbit, with no adjustable parameters, which has not proved possible previously. We show that the asymptotic analysis compares very favourably with numerical results.Comment: 24 pages, 3 figures, submitted to Nonlinearit

Evolution of emotions on networks leads to the evolution of cooperation in social dilemmas

We show that the resolution of social dilemmas in random graphs and scale-free networks is facilitated by imitating not the strategy of better-performing players but, rather, their emotions. We assume sympathy and envy to be the two emotions that determine the strategy of each player in any given interaction, and we define them as the probabilities of cooperating with players having a lower and a higher payoff, respectively. Starting with a population where all possible combinations of the two emotions are available, the evolutionary process leads to a spontaneous fixation to a single emotional profile that is eventually adopted by all players. However, this emotional profile depends not only on the payoffs but also on the heterogeneity of the interaction network. Homogeneous networks, such as lattices and regular random graphs, lead to fixations that are characterized by high sympathy and high envy, while heterogeneous networks lead to low or modest sympathy but also low envy. Our results thus suggest that public emotions and the propensity to cooperate at large depend, and are in fact determined by, the properties of the interaction network

Co-evolution of strategy and structure in complex networks with dynamical linking

Here we introduce a model in which individuals differ in the rate at which they seek new interactions with others, making rational decisions modeled as general symmetric two-player games. Once a link between two individuals has formed, the productivity of this link is evaluated. Links can be broken off at different rates. We provide analytic results for the limiting cases where linking dynamics is much faster than evolutionary dynamics and vice-versa, and show how the individual capacity of forming new links or severing inconvenient ones maps into the problem of strategy evolution in a well-mixed population under a different game. For intermediate ranges, we investigate numerically the detailed interplay determined by these two time-scales and show that the scope of validity of the analytical results extends to a much wider ratio of time scales than expected

A multi-stage fluidized bed system for Continuous CO2 capture by means of temperature swing adsorption – First results from bench scale experiments

Temperature swing adsorption processes have been proposed as an alternative to common amine scrubbing processes for CO2 capture from stack flue-gas streams, as they have the potential to reduce the overall capture costs significantly. In the recent years, researchers have put a great effort into the development of highly selective CO2 adsorbent materials with sufficiently large CO2 transport capacities and cyclic operating stability. However, comparably little work has been attributed to the development of suitable reactor designs or to the experimental study of continuously operated temperature swing adsorption (TSA) processes that utilizes those adsorbent materials. The authors of this work most recently introduced a reactor system that allows for effective and efficient operation of the TSA process. The system comprises two interconnected multi-stage fluidized bed columns that enable counter-current contact of adsorbent and gas streams in both columns whilst allowing for effective heat management through indirect heat exchange in each stage. Based on the proposed reactor design, a fully integrated bench scale unit (BSU) has been constructed and put into operation to deliver a proof of concept and to further study the process experimentally (see Figure 6). Each of the BSU columns comprises five fluidized bed stages that are operated in the bubbling bed regime. Transport of solids between the two columns is carried out in two transport loops consisting of a screw conveyor, a riser and a gravitational gas/solids separator each. An amine-functionalized solid sorbent selectively adsorbs CO2 in the adsorber at low temperature and is subsequently regenerated in the desorber column at higher operating temperature, before it is returned to the adsorber. This work presents results obtained from the first continuous CO2 capture experiment within the unit. Please click Additional Files below to see the full abstract

Fluid-dynamic study on a multi-stage fluidized bed column for continuous CO2 capture via temperature swing adsorption

Adsorption based processes have a great potential to significantly reduce the overall costs of CO2 separation from stack flue gas as compared to currently available technologies. One of the main challenges in the development of these processes is certainly the provision of adequate adsorbents. Hence, in the last decade a great effort has been put into screening and testing of various adsorbent materials. However, beside the identification of suitable adsorbent materials it is of equal importance to develop suitable reactor designs that allow for effective and most cost efficient utilization of these materials and so far only little work has been attributed to this subject. Nevertheless, it was shown that for thermodynamic reasons it is essential to provide counter-current contact between adsorbent and gas streams in order to allow for efficient operation of any Temperature Swing Adsorption (TSA) CO2 capture process. It was further highlighted that effective heat transfer with the used adsorbent material is necessary as the reported values of their corresponding adsorption enthalpies are typically rather large. Please click Additional Files below to see the full abstract

Two-population replicator dynamics and number of Nash equilibria in random matrix games

We study the connection between the evolutionary replicator dynamics and the number of Nash equilibria in large random bi-matrix games. Using techniques of disordered systems theory we compute the statistical properties of both, the fixed points of the dynamics and the Nash equilibria. Except for the special case of zero-sum games one finds a transition as a function of the so-called co-operation pressure between a phase in which there is a unique stable fixed point of the dynamics coinciding with a unique Nash equilibrium, and an unstable phase in which there are exponentially many Nash equilibria with statistical properties different from the stationary state of the replicator equations. Our analytical results are confirmed by numerical simulations of the replicator dynamics, and by explicit enumeration of Nash equilibria.Comment: 9 pages, 2x2 figure

Statistical mechanics of ecosystem assembly

We introduce a toy model of ecosystem assembly for which we are able to map out all assembly pathways generated by external invasions. The model allows to display the whole phase space in the form of an assembly graph whose nodes are communities of species and whose directed links are transitions between them induced by invasions. We characterize the process as a finite Markov chain and prove that it exhibits a unique set of recurrent states (the endstate of the process), which is therefore resistant to invasions. This also shows that the endstate is independent on the assembly history. The model shares all features with standard assembly models reported in the literature, with the advantage that all observables can be computed in an exact manner.Comment: Accepted for publication in Physical Review Letter

Equilibrium states for potentials with \sup\phi - \inf\phi < \htop(f)

In the context of smooth interval maps, we study an inducing scheme approach to prove existence and uniqueness of equilibrium states for potentials $\phi$ with he `bounded range' condition \sup \phi - \inf \phi < \htop, first used by Hofbauer and Keller. We compare our results to Hofbauer and Keller's use of Perron-Frobenius operators. We demonstrate that this `bounded range' condition on the potential is important even if the potential is H\"older continuous. We also prove analyticity of the pressure in this context.Comment: Added Lemma 6 to deal with the disparity between leading eigenvalues and operator norms. Added extra references and corrected some typo