Introduction to focus issue: design and control of self-organization in distributed active systems

Mode Selection in Compressible Active Flow Networks

Coherent, large-scale dynamics in many nonequilibrium physical, biological, or information transport networks are driven by small-scale local energy input. Here, we introduce and explore an analytically tractable nonlinear model for compressible active flow networks. In contrast to thermally driven systems, we find that active friction selects discrete states with a limited number of oscillation modes activated at distinct fixed amplitudes. Using perturbation theory, we systematically predict the stationary states of noisy networks and find good agreement with a Bayesian state estimation based on a hidden Markov model applied to simulated time series data. Our results suggest that the macroscopic response of active network structures, from actomyosin force networks to cytoplasmic flows, can be dominated by a significantly reduced number of modes, in contrast to energy equipartition in thermal equilibrium. The model is also well suited to study topological sound modes and spectral band gaps in active matter.

Energy scaling of targeted optimal control of complex networks

Recently it has been shown that the control energy required to control a dynamical complex network is prohibitively large when there are only a few control inputs. Most methods to reduce the control energy have focused on where, in the network, to place additional control inputs. Here, in contrast, we show that by controlling the states of a subset of the nodes of a network, rather than the state of every node, while holding the number of control signals constant, the required energy to control a portion of the network can be reduced substantially. The energy requirements exponentially decay with the number of target nodes, suggesting that large networks can be controlled by a relatively small number of inputs as long as the target set is appropriately sized. We validate our conclusions in model and real networks to arrive at an energy scaling law to better design control objectives regardless of system size, energy restrictions, state restrictions, input node choices and target node choices.

The energy required to control a dynamical complex network can be prohibitively large when there are only a few control inputs. Here the authors demonstrate that if only a subset of the network is targeted the energy requirements decrease exponentially.

Optimal control of complex networks: Balancing accuracy and energy of the control action

Recently, it has been shown that the control energy required to control a large dynamical complex network is prohibitively large when there are only a few control inputs. Most methods to reduce the control energy have focused on where, in the network, to place additional control inputs. We also have seen that by controlling the states of a subset of the nodes of a network, rather than the state of every node, the required energy to control a portion of the network can be reduced substantially. The energy requirements exponentially decay with the number of target nodes, suggesting that large networks can be controlled by a relatively small number of inputs as long as the target set is appropriately sized. Here, we see that the control energy can be reduced even more if the prescribed final states are not satisfied strictly. We introduce a new control strategy called balanced control for which we set our objective function as a convex combination of two competitive terms: (i) the distance between the output final states at a given final time and given prescribed states and (ii) the total control energy expenditure over the given time period. We also see that the required energy for the optimal balanced control problem approximates the required energy for the optimal target control problem when the coefficient of the second term is very small. We validate our conclusions in model and real networks regardless of system size, energy restrictions, state restrictions, input node choices, and target node choices.

From chemical systems to systems chemistry: Patterns in space and time

We present a brief, idiosyncratic overview of the past quarter century of progress in nonlinear chemical dynamics and discuss what we view as the most exciting recent developments and some challenges and likely areas of progress in the next 25 years.

Novel type of amplitude spiral wave in a two-layer system

Interaction of spiral waves in a two-layer system described by a model of coupled complex Ginzburg-Landau equations with negative-feedback couplings ε(1) and ε(2) is studied. Synchronization of two spiral waves can be broadly found if ε(1)+ε(2) is sufficiently large. Prior to the synchronization, under the condition of strongly asymmetric coupling (∣ε(1)-ε(2)∣≫0), a novel type of spiral wave, amplitude spiral wave, exists in the driven system. The pattern of amplitude spiral wave shows the spiral in the amplitude and without a singularity point (tip), compared to usual spiral waves known for phase with amplitude uniform far away from tips and rotating around tips.

Emergent, collective oscillations of self-mobile particles and patterned surfaces under redox conditions

We have discovered that silver chloride (AgCl) particles in the presence of UV light and dilute hydrogen peroxide exhibit both single-particle and collective oscillations in their motion which arise due to an oscillatory, reversible conversion of AgCl to silver metal at the particle surface. This system exhibits several of the hallmarks of nonlinear oscillatory reactions, including bistability, reaction waves, and synchronized collective oscillations at high particle concentrations. However, unlike traditional oscillatory reactions that take place among dispersed solute species in solution or near a fixed electrode surface, this system of self-mobile catalytic particles evinces a new dynamical length scale: the interparticle spacing, which appears to control wave propagation. The collective motions of these powered nanoparticles self-organize into clumped oscillators with significant spatiotemporal correlations between clumps. A variant of this system using a regular array of lithographically patterned silver disks supports the propagation of binary "On/Off" Ag/AgCl waves through the lattice.