Controlling complex networks is of paramount importance in science and engineering. Despite the recent development of structural controllability theory, we continue to lack a framework to control undirected complex networks, especially given link weights. Here we introduce an exact controllability paradigm based on the maximum multiplicity to identify the minimum set of driver nodes required to achieve full control of networks with arbitrary structures and link-weight distributions. The framework reproduces the structural controllability of directed networks characterized by structural matrices. We explore the controllability of a large number of real and model networks, finding that dense networks with identical weights are difficult to be controlled. An efficient and accurate tool is offered to assess the controllability of large sparse and dense networks. The exact controllability framework enables a comprehensive understanding of the impact of network properties on controllability, a fundamental problem towards our ultimate control of complex systems.

An extremely challenging problem of significant interest is to predict catastrophes in advance of their occurrences. We present a general approach to predicting catastrophes in nonlinear dynamical systems under the assumption that the system equations are completely unknown and only time series reflecting the evolution of the dynamical variables of the system are available. Our idea is to expand the vector field or map of the underlying system into a suitable function series and then to use the compressive-sensing technique to accurately estimate the various terms in the expansion. Examples using paradigmatic chaotic systems are provided to demonstrate our idea and potential challenges are discussed.It has been recognized that nonlinear dynamics are ubiquitous in many natural and engineering systems. A nonlinear system, in its parameter space, can often exhibit catastrophic bifurcations that ruin the desirable or 'normal" state of operation. Consider, for example, the phenomenon of crisis [1] where, as a system parameter is changed, a chaotic attractor collides with its own basin boundary and is suddenly destroyed. After the crisis, the state of the system is completely different from that on the attractor before the crisis. Suppose that, for a nonlinear dynamical system, the state before the crisis is normal and desirable, and the state after the crisis is undesirable or destructive. The crisis can thus be regarded as a catastrophe that one strives to avoid at all cost. Catastrophic events, of course, can occur in different forms in all kinds of natural and man-made systems. A question of paramount importance is how to predict catastrophes in advance of their possible occurrences. This is especially challenging when the equations of the underlying dynamical system are unknown and one must then rely on measured time series or data to predict any potential catastrophe.In this paper, we articulate a strategy to address the problem of predicting catastrophes in nonlinear dynamical systems. We assume that an accurate model of the system is not available, i.e., the system equations are unknown, but the time evolutions of the key Europe PMC Funders Author ManuscriptsEurope PMC Funders Author Manuscripts variables of the system can be accessed through monitoring or measurements. Our method consists of three steps: (i) predicting the dynamical system based on time series, (ii) identifying the parameters of the system, and (iii) performing bifurcation analysis using the predicted system equations to locate potential catastrophic events in the parameter space so as to determine the likelihood of system's drifting into a catastrophe regime. In particular, if the system operates at a parameter setting close to such a critical bifurcation, catastrophe is imminent as a small parameter change or a random perturbation can push the system beyond the bifurcation point. To be concrete, in this paper we regard crises as catastrophes. Once a complete set of system equations has been predicted and the parameters have been id...

We study the relationship between dynamical properties and interaction patterns in complex oscillator networks in the presence of noise. A striking finding is that noise leads to a general, one-to-one correspondence between the dynamical correlation and the connections among oscillators for a variety of node dynamics and network structures. The universal finding enables an accurate prediction of the full network topology based solely on measuring the dynamical correlation. The power of the method for network inference is demonstrated by the high success rate in identifying links for distinct dynamics on both model and real-life networks. The method can have potential applications in various fields due to its generality, high accuracy, and efficiency.

Our ability to uncover complex network structure and dynamics from data is fundamental to understanding and controlling collective dynamics in complex systems. Despite recent progress in this area, reconstructing networks with stochastic dynamical processes from limited time series remains to be an outstanding problem. Here we develop a framework based on compressed sensing to reconstruct complex networks on which stochastic spreading dynamics take place. We apply the methodology to a large number of model and real networks, finding that a full reconstruction of inhomogeneous interactions can be achieved from small amounts of polarized (binary) data, a virtue of compressed sensing. Further, we demonstrate that a hidden source that triggers the spreading process but is externally inaccessible can be ascertained and located with high confidence in the absence of direct routes of propagation from it. Our approach thus establishes a paradigm for tracing and controlling epidemic invasion and information diffusion in complex networked systems.