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Are there known complex systems that exhibit fragility in the sense that small perturbations — either in the local interaction rules between particles (or agents), or in the surrounding environment — can lead to major changes in global behavior?

My question is not about chaos (extreme sensitivity of such systems to initial conditions). Rather, I am interested in a different phenomenon: regime transitions in the macroscopic behavior of complex systems composed of many locally interacting agents. It is more about changes in the interaction rules, rather than initial conditions.

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    $\begingroup$ is this not called chaos? Small changes in the initial conditions lead to vastly different outcomes? $\endgroup$ Commented Nov 7 at 14:17
  • $\begingroup$ Chaos can be observed in more traditional dynamical systems, such as the Lorenz system (a three-dimensional system of ordinary differential equations), which illustrates the difficulty of making meteorological predictions. This is due to the extreme sensitivity of such systems to initial conditions. However, my question is not about this type of chaos. Rather, I am interested in a different phenomenon: regime transitions in the macroscopic behavior of complex systems composed of many locally interacting agents. It is more about changes in the interaction rules, rather than initial conditions. $\endgroup$ Commented Nov 7 at 14:58
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    $\begingroup$ @megaproba you may be interested in learning about the theory of phase transitions (see the textbooks by Pathria & Beale, Kardar volume 2, Amit et al, Baxter, etc.) In the context of materials science, it might be more appropriate to think of 'fragility' as a sort of irreversible (or sensitive) plasticity than what you describe. $\endgroup$ Commented Nov 7 at 18:01

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Since in the comments the OP clarifies they don't mean fragility in the sense of sensitivity to initial conditions (classical chaos), but rather

regime transitions in the macroscopic behavior of complex systems composed of many locally interacting agents. It is more about changes in the interaction rules, rather than initial conditions

then the closest concept is perhaps that of phase transitions, e.g., in magnetic systems (where its macroscopic magnetism changes as the coupling between individual spins or an external magnetic field varies), but also between states of matter (as, say, temperature or pressure changes), among many others.

These transitions can be linked to bifurcations, which are virtually ubiquitous in dynamical systems. And also the concept of structural instability should be mentioned, since it deals with how resistant a system is to perturbations (in the abstract space of dynamical systems).

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