Network resilience

Abstract

Many systems on our planet are known to shift abruptly and irreversibly from one state to another when they are forced across a "tipping point," such as mass extinctions in ecological networks, cascading failures in infrastructure systems, and social convention changes in human and animal networks. Such a regime shift demonstrates a system's resilience that characterizes the ability of a system to adjust its activity to retain its basic functionality in the face of internal disturbances or external environmental changes. In the past 50 years, attention was almost exclusively given to low dimensional systems and calibration of their resilience functions and indicators of early warning signals without considerations for the interactions between the components. Only in recent years, taking advantages of the network theory and lavish real data sets, network scientists have directed their interest to the real-world complex networked multidimensional systems and their resilience function and early warning indicators. This report is devoted to a comprehensive review of resilience function and regime shift of complex systems in different domains, such as ecology, biology, social systems and infrastructure. We cover the related research about empirical observations, experimental studies, mathematical modeling, and theoretical analysis. We also discuss some ambiguous definitions, such as robustness, resilience, and stability.

Accuracy of a one-dimensional reduction of dynamical systems on networks

“…respectively. The Gao's reduction is exact for uncorrelated networks when all of R (1) , R (2) , and 3) are equal to 1.…”

“…A definition of resilience is the property of the system to be able to adjust its activity to retain its functionality when some error or failure occurs [1][2][3][4]. Ecology [5,6], human physiology [7], cell biology [8], food security [9,10], finance [11,12], and psychopathology [13,14] are some of the areas where the resilience of systems has been studied.…”

“…The occurrence of such critical regime shifts bears some universality but depends on the type of dynamics and perturbations applied. Quantitatively anticipation of critical regime shifts in complex dynamical systems has been actively studied [3,[23][24][25][26].…”

“…For an ecosystem, a drastic change is typically from a stable equilibrium corresponding to the coexistence of various species to a mass extinction of several species [27,28]. Crucially, the size of the perturbation that a dynamical system on a network can tolerate, which is an operational definition of the network resilience [3], depends on the structure of the network. For example, a change in the network structure induced by the removal of a fraction of nodes and the associated edges may decrease the resilience of the system [29][30][31].…”

Network resilience in the presence of non-equilibrium dynamics

“…Determining such sudden transitions is relatively easy when a species or an isolated system governs the state of a system. However, for complex networked systems where many nodes interact, e.g., genetic networks, neural networks, and ecological networks of interacting species -sudden transitions are highly unpredictable [15,16]. This is because current analytical frameworks of measuring resilience are mostly limited to low-dimensional systems and are underdeveloped for high-dimensional systems, where multiple components simultaneously interact through a complex network.…”