Temporal inactivation enhances robustness in an evolving system

TL;DR

This paper investigates how temporary inactivation of elements in an evolving system can enhance its robustness, showing that allowing elements to survive in inactive states for longer periods helps resist disruptive influences.

Contribution

It introduces a dynamic model demonstrating that increased inactivation time limits improve system robustness against new element inclusion and attacks.

Findings

Larger inactivation time $T_W$ increases robustness.

The system exhibits both growing and non-growing phases.

Inactivation allows elements to survive adverse conditions.

Abstract

We study the robustness of an evolving system that is driven by successive inclusions of new elements or constituents with $m$ random interactions to older ones. Each constitutive element in the model stays either active or is temporarily inactivated depending upon the influence of the other active elements. If the time spent by an element in the inactivated state reaches $T_W$, it gets extinct. The phase diagram of this dynamic model as a function of $m$ and $T_W$ is investigated by numerical and analytical methods and as a result both growing (robust) as well as non-growing (volatile) phases are identified. It is also found that larger time limit $T_W$ enhances the system's robustness against the inclusion of new elements, mainly due to the system's increased ability to reject "falling-together" type attacks. Our results suggest that the ability of an element to survive in an unfavorable situation for a while, either as a minority or in a dormant state, could improve the robustness of the entire system.