For many years, researchers assumed that a network would behave more reliably if its individual parts behaved as similarly as possible. However, real systems are rarely that orderly. Generators operate differently, neurons have different shapes and behaviors, species play different roles within ecosystems, and components in engineered materials are not always completely homogeneous.

Physicists at Northwestern University now say these differences may be an advantage rather than a disadvantage.

How disorder can increase network stability

In a new study, researchers created a mathematical framework to determine when fluctuations that scientists often describe as disorder or chaos can make networks more stable. Their results suggest that many physical, engineered, and biological systems can become more resilient when their components or connections are not identical.

The finding challenges the idea that uniformity should always be the goal. Instead, carefully introducing differences into a system could help engineers design more resilient power grids, advanced materials, and other interconnected technologies. The research may also help explain why irregularities are so common in neural, biological, and ecological networks.

The study was published September 17 in Science. The researchers also developed a website that allows users to visually explore the framework. By adjusting different parameters, users can observe how network components interact, synchronize, and form organized patterns.

“Previous research has shown that in increasing numbers of cases, disorder—also known as heterogeneity, irregularity, or asymmetry—across the nodes of a network can actually improve stability and desired behavior,” said Northwestern’s Adilson Motter, who led the study. “We’ve seen this in important real-world systems like power grids, metamaterials, and brain computation. But we didn’t know how widespread this effect was or what types of systems could benefit from it. Our new research answers these questions, explains why these differences can improve stability, and even reveals why scientists have overlooked this effect for so long.”

Motter is the Charles E. and Emma H. Morrison Professor of Physics and Astronomy and director of the Center for Network Dynamics in Northwestern University’s Weinberg College of Arts and Sciences. Northwestern postdoctoral researcher Arthur Montanari and graduate student Pietro Zanin, both members of the Motter group, are co-first authors of the study.

Why traditional network models missed the effect

Many interconnected systems survive only if they can recover from disruption. Strong gusts of wind can tear a herd apart, a sudden spike in electricity demand can strain a power grid, and an impact can deform a material.

Scientists often represent these systems as networks made up of individual components called nodes, connected by links. In a power grid, generators act as nodes and transmission lines form the links between them. In ecological networks, species are nodes, while relationships such as competition, cooperation, and predation form the links.

Traditionally, researchers have focused on how these nodes are connected. Many studies also rely on simplified mathematical models, including the widely used Kuramoto model, in which each node is represented by only one variable.

Although these simplified approaches have generated valuable insights, they may leave out important behaviors found in real-world systems, where individual components and their interactions can be much more complex.

“Real systems are rarely homogeneous,” Montanari said. “Birds have different personalities, neurons have different shapes, and even human social relationships can be asymmetrical. These differences may seem random, but they can have profound effects on the behavior of the entire system.”

Earlier research suggested that these differences could be beneficial in some situations. In 2020, research by Motter’s team published in Nature Physics showed that generators could synchronize more effectively when they operated somewhat differently from one another. In 2025, a study led by Montanari in Nature Communications found comparable effects in a model involving swarm behavior and drone swarms.

What remained unclear was whether these examples were rare exceptions or evidence of a broader principle.

“Disorder can stabilize a network, but only if the node dynamics are sufficiently rich,” Motter said. “Simplified models can inadvertently remove the stabilizing effects we want to capture.”

Finding the right amount of variation

To investigate the question more broadly, the researchers developed a mathematical framework capable of describing more realistic network behavior.

They first examined a system close to a steady state. The researchers then calculated what happened after introducing a small disturbance. When disturbances gradually disappeared, the system returned to stability. As disturbances became larger, the system eventually became unstable.

The team compared networks made up of identical components with networks containing differences in their components or connections. This allowed the researchers to identify situations in which heterogeneity could provide greater stability than homogeneity.

Motter and his colleagues tested the framework using models of power grids, neurons, swarms, engineered materials, and ecological networks.

They found that disorder can improve stability in two main ways. Differences can exist between the nodes themselves or in the links connecting those nodes. The effects also depend on where the changes occur and how large they are.

A moderate level of disorder can make a network more stable, but excessive fluctuations can eventually push the same system in the opposite direction.

“If you make the system more homogeneous, you lose stability,” Montanari said. “However, when disorder increases too much, stability also disappears. Our framework helps pinpoint the level of disorder that helps the system achieve optimal stability.”

Random variation may be enough

The researchers also found that beneficial differences do not always need to be carefully designed in advance.

In many of their models, randomly introduced fluctuations produced better stability than the optimal fully uniform configuration. This suggests that simply allowing some diversity within a system may provide benefits.

One important exception occurred when fluctuations affected the links connecting nodes rather than the nodes themselves. In those cases, even networks with relatively simple node dynamics could gain stability from disorder.

Why does nature favor imperfect networks?

The discovery could help researchers better understand existing complex systems, particularly ecological networks, while giving engineers new strategies for designing systems from the ground up.

One long-standing mystery in ecology is that older mathematical models predicted that large, complex ecosystems should be inherently unstable. Yet nature contains many highly diverse and persistent ecosystems.

“Since the 1970s, mathematical models have predicted that large, complex ecosystems should become unstable and collapse,” Montanari said. “However, very large and highly diverse ecosystems persist in nature. Our findings suggest that variation in mutually beneficial interactions, such as those between pollinators and flowers, may help explain this discrepancy.”

Could controlled disorder improve advanced materials?

The same principles may eventually influence the design of advanced materials.

Building materials are often constructed from repeating, nearly identical units. The new findings suggest that engineers may be able to create different or improved behaviors by intentionally changing the shape, size, orientation, and physical properties of those units.

To do this effectively, researchers must treat these materials as mechanical networks and use models detailed enough to preserve the system’s real dynamics. Computational techniques can then be used to search for combinations of variations that produce the greatest benefits.

“If disorder increases stability, the next challenge is to find a way to optimally design it,” Motter said.

This study, titled “Stability Promoted by Disability,” was supported by the Army Research Office through Grant No. W911NF-22-2-0109 and the National Science Foundation through Grant No. DMS-2308341. The research also acknowledges the stimulating research environment provided by the NSF-Simons National Institute for Biological Theoretical Mathematics, supported by NSF Grant No. DMS-2235451 and Simons Foundation Grant No. MP-TMPS-00005320.