Dynamics in a Bistable-Element-Network with Delayed Coupling and Local Noise

The dynamics of an ensemble of bistable elements under the influence of noise and with global time-delayed coupling is studied numerically by using a Langevin description and analytically by using 1) a Gaussian approximation and 2) a dichotomous model. We find that for a strong enough positive feedback the system undergoes a phase transition and adopts a non-zero stationary mean field. A variety of coexisting oscillatory mean field states are found for positive and negative couplings. The magnitude of the oscillatory states is maximal for a certain noise temperature, i.e., the system demonstrates the phenomenon of coherence resonance. While away form the transition points the system dynamics is well described by the Gaussian approximation, near the bifurcations it is more adequately described by the dichotomous model.Comment: 2 pages, 2 figures. To be published in the proceedings of "The 3rd International Symposium on Slow Dynamics in Complex Systems", eds. M. Tokuyama, I. Oppenheim, AIP Conf. serie

Co-Repressive Interaction and Clustering of Degrade-and-Fire Oscillators

International audienceStrongly nonlinear degrade-and-fire (DF) oscillations may emerge in genetic circuits having a delayed negative feedback loop as their core element. Here we study the synchronization of DF oscillators coupled through a common repressor field. For weak coupling, initially distinct oscillators remain de-synchronized. For stronger coupling, oscillators can be forced to wait in the repressed state until the global repressor field is sufficiently degraded, and then they fire simultaneously forming a synchronized cluster. Our analytical theory provides necessary and sufficient conditions for clustering and specifies the maximum the number of clusters which can be formed in the asymptotic regime. We find that in the thermodynamic limit a phase transition occurs at a certain coupling strength from the weakly-clustered regime with only microscopic clusters to a strongly clustered regime when at least one giant cluster has to be present

Optimal serverless networks attacks, complexity and some approximate algorithms

A network attack is a set of network elements that are disabled by an adversary. The goal for the attack is to produce the most possible damage to the network in terms of network connectivity by disabling the least possible number of network elements. We show that the problem of finding the optimal attack in a serverless network is NP-Complete even when only edges or nodes are considered for disabling. We study a node attack policy with polynomial complexity based on shorter paths and show that this attack policy outperforms in most cases classical attacks policies such as random attack or maximum degree attack. We also study the behavior of different network topologies under these attack policies