arXiv subjects

Margarita Ifti

Publications and source records attributed to Margarita Ifti.

4 recordsLinked to original sources

arXiv2014

Phase Transitions in Systems of Interacting Species

We discuss an autocatalytic reaction system: the cyclic competition model A1 + A2 --> 2 A2, A2 + A3 --> 2 A3, A3 + A4 --> 2 A4, A4 + A1 --> 2 A1), as well as its neutral counterpart. Migrations are introduced into the model. When stochastic phenomena are taken into account, a phase transition between a ``fixation'' and a ``neutral'' regime is observed. In the ``fixation'' regime, species A1 and A3 form an alliance against species A2 and A4, and the final state is one in which one of the symbiotic pairs has won. The odd--even ``coarse--grained'' systems is mapped onto the two--species neutral (Kimura) model. In the ``neutral'' regime, all four species survive for long (evolutionary) times. The analytical results are checked against computer simulations of the model. The model is generalized for n species. Also, a generalized version of the Volterra model is analysed.

q-bio.PE↗

arXiv2004

Effects of neighbourhood size and connectivity on spatial Continuous Prisoner's Dilemma

The Prisoner's Dilemma, a 2-person game in which the players can either cooperate or defect, is a common paradigm for studying the evolution of cooperation, when individuals exhibit variable degrees of cooperation. It is known that in the presence of spatial structure, when individuals ``play against'' their neighbours, and ``compare to'' them, cooperative investments can evolve to considerable levels. Here we examine the effect of increasing the neighbourhood size: we find that the mean-field limit of no cooperation is reached for a critical neighbourhood size of about five neighbours. We also find the related result that in a network of players, the critical average degree (number of neighbours) of nodes for which defection is the final state depends only on the network topology. This critical average degree is considerably higher for clustered networks, than for distributed random networks. This result strengthens the argument that clustering is the mechanism which makes the development and maintenance of the cooperation possible.

q-bio.PE↗

arXiv2004

Crossover Behaviour of 3-Species Systems with Mutations or Migrations

We study the ABC model in the cyclic competition and neutral drift versions, with mutations and migrations introduced into the model. When stochastic phenomena are taken into account, there are three distinct regimes in the model. (i) In the "fixation" regime, the first extinction time scales with the system size N and has an exponential distribution, with an exponent that depends on the mutation/migration probability per particle. (ii) In the "diversity" regime, the order parameter remains nonzero for very long times, and becomes zero only rarely, almost never for large system sizes. (iii) In the critical regime, the first extinction time has a power-law distribution with exponent -1. The transition corresponds to a crossover from diffusive behaviour to Gaussian fluctuations about a stable solution. The analytical results are checked against computer simulations of the model.

nlin.AO↗

arXiv2003

Survival and Extinction in Cyclic and Neutral Three--Species Systems

We study the ABC model (A + B --> 2B, B + C --> 2C, C + A --> 2A), and its counterpart: the three--component neutral drift model (A + B --> 2A or 2B, B + C --> 2B or 2C, C + A --> 2C or 2A.) In the former case, the mean field approximation exhibits cyclic behaviour with an amplitude determined by the initial condition. When stochastic phenomena are taken into account the amplitude of oscillations will drift and eventually one and then two of the three species will become extinct. The second model remains stationary for all initial conditions in the mean field approximation, and drifts when stochastic phenomena are considered. We analyzed the distribution of first extinction times of both models by simulations and from the point of view of the Fokker-Planck equation. Survival probability vs. time plots suggest an exponential decay. For the neutral model the extinction rate is inversely proportional to the system size, while the cyclic model exhibits anomalous behaviour for small system sizes. In the large system size limit the extinction times for both models will be the same. This result is compatible with the smallest eigenvalue obtained from the numerical solution of the Fokker-Planck equation. We also studied the long--time behaviour of the probability distribution. The exponential decay is found to be robust against certain changes, such as the three reactions having different rates.

nlin.AO↗