Autonomous Learning by Simple Dynamical Systems with Delayed Feedbacks

A general scheme for construction of dynamical systems able to learn generation of the desired kinds of dynamics through adjustment of their internal structure is proposed. The scheme involves intrinsic time-delayed feedback to steer the dynamics towards the target performance. As an example, a system of coupled phase oscillators, which can by changing the weights of connections between its elements evolve to a dynamical state with the prescribed (low or high) synchronization level, is considered and investigated

Hydrodynamic collective effects of active proteins in biological membranes

Lipid bilayers forming biological membranes are known to behave as viscous 2D fluids on submicrometer scales; usually they contain a large number of active protein inclusions. Recently, it has been shown [Proc. Nat. Acad. Sci. USA 112, E3639 (2015)] that such active proteins should in- duce non-thermal fluctuating lipid flows leading to diffusion enhancement and chemotaxis-like drift for passive inclusions in biomembranes. Here, a detailed analytical and numerical investigation of such effects is performed. The attention is focused on the situations when proteins are concentrated within lipid rafts. We demonstrate that passive particles tend to become attracted by active rafts and are accumulated inside them.Comment: 12 pages, 7 figure

Towards active microfluidics: Interface turbulence in thin liquid films with floating molecular machines

Thin liquid films with floating active protein machines are considered. Cyclic mechanical motions within the machines, representing microscopic swimmers, lead to molecular propulsion forces applied to the air-liquid interface. We show that, when the rate of energy supply to the machines exceeds a threshold, the flat interface becomes linearly unstable. As the result of this instability, the regime of interface turbulence, characterized by irregular traveling waves and propagating machine clusters, is established. Numerical investigations of this nonlinear regime are performed. Conditions for the experimental observation of the instability are discussed.Comment: 9 pages, 8 figures, RevTeX, submitted to Physical Review

Self-propulsion through symmetry breaking

In addition to self-propulsion by phoretic mechanisms that arises from an asymmetric distribution of reactive species around a catalytic motor, spherical particles with a uniform distribution of catalytic activity may also propel themselves under suitable conditions. Reactive fluctuation-induced asymmetry can give rise to transient concentration gradients which may persist under certain conditions, giving rise to a bifurcation to self-propulsion. The nature of this phenomenon is analyzed in detail, and particle-level simulations are carried out to demonstrate its existence.Comment: 6 pages, 3 figures. Appeared in EPL (Europhysics Letters

Replica-symmetry breaking in dynamical glasses

Systems of globally coupled logistic maps (GCLM) can display complex collective behaviour characterized by the formation of synchronous clusters. In the dynamical clustering regime, such systems possess a large number of coexisting attractors and might be viewed as dynamical glasses. Glass properties of GCLM in the thermodynamical limit of large system sizes $N$ are investigated. Replicas, representing orbits that start from various initial conditions, are introduced and distributions of their overlaps are numerically determined. We show that for fixed-field ensembles of initial conditions, as used in previous numerical studies, all attractors of the system become identical in the thermodynamical limit up to variations of order $1/\sqrt{N}$ because the initial value of the coupling field is characterized by vanishing fluctuations, and thus replica symmetry is recovered for $N\to \infty$. In contrast to this, when random-field ensembles of initial conditions are chosen, replica symmetry remains broken in the thermodynamical limit.Comment: 19 pages, 18 figure