arXiv subjects

Adilson E. Motter

Publications and source records attributed to Adilson E. Motter.

At least 19 recordsLinked to original sources

arXiv2026

Quantum manifestations of converse symmetry breaking

Quantum synchronization holds promise in advancing quantum technologies such as sensing, communication, and computation. A key challenge in this rapidly developing field is to identify mechanisms that can promote the emergence of synchronous dynamics. Here, we show that quantum synchronization can be enhanced by introducing controlled heterogeneity in the form of coupling mismatches. Using spin van der Pol oscillators as a model system, we show that this mechanism constitutes a quantum analog of the phenomenon of converse symmetry breaking previously identified in classical oscillator networks, where a synchronous state is stabilized by explicit symmetry breaking. We quantify how quantum effects modify this behavior by tuning the degree of quantumness through variations of the spin quantum number. These findings suggest that quantum synchronization can be enhanced in experiments by harnessing rather than suppressing heterogeneity.

quant-ph↗

arXiv2026

Learning infinite context windows in recurrent architectures via spatial neural computing

Recurrent neural networks (RNNs) offer linear-time scaling with sequence length while requiring only constant memory, yet they struggle to capture long-range dependencies due to vanishing gradients and limited receptive fields. To address these limitations, we introduce a second-order recurrent model in which the standard neuron-to-neuron communication is replaced by a spatially evolving field governed by (discretized) partial differential equations. Drawing inspiration from the role of cortical waves in brain computation, this mechanism allows structured spatiotemporal patterns to serve as an implicit, high-capacity memory. We show that the resulting model is equivalent to a structured infinite-order RNN in which the current state depends explicitly on its entire history of past states, yielding an effectively unbounded receptive field with a fixed number of parameters. We further derive constructive conditions to ensure marginal stability, constraining the gradient spectrum on the unit circle and thereby eliminating vanishing and exploding gradients. Empirically, the proposed architecture outperforms other recurrent models on long-horizon benchmarks while using substantially fewer parameters, demonstrating that spatial dynamics can effectively bridge the gap between efficient inference and long-term memory.

cs.LG↗

arXiv2026

Disorder-promoted stability

Previous studies of network dynamics have suggested that heterogeneity among nodes inhibits stability, at odds with the ubiquity of inherently heterogeneous natural and engineered systems. Here, we show that this conclusion arises from model reductions introduced for mathematical tractability and breaks down when nodal dynamics are higher-dimensional, yielding non-Hermitian Jacobians. In such systems, including neural, power-grid, and material networks, nodal heterogeneity can instead enhance stability, even when parameters are randomly disordered. Non-Hermiticity also underlies the stabilizing effects of network heterogeneity, which can arise even in one-dimensional nodal dynamics through nonreciprocal interactions, as shown for ecological networks. Our framework reveals disorder not as a liability but as a general resource for stabilizing complex systems.

cond-mat.dis-nn↗

arXiv2026

Generalized Master Stability of Heterogeneous Delay-Coupled Networks

Time delays are ubiquitous in physical and biological networked systems, playing a fundamental role in the emergence and stability of collective behavior. Yet, existing theoretical methods for synchronization analysis of delay-coupled systems are largely limited to networks with homogeneous degree distributions. Here, we extend the master stability function framework to a broad class of degree-heterogeneous, weighted, and directed delay-coupled networks. The analysis reveals that synchronization can be enhanced in heterogeneous networks compared to homogeneous ones, including all-to-all networks, which are known to be optimal in non-delayed systems. To identify optimal heterogeneous structures, we develop a network optimization method that finds directional, edge-weighted configurations maximizing synchronization stability. Our results show that, in delay-coupled networks, heterogeneity and nonreciprocity are key resources for synchronization.

nlin.AO↗

arXiv2026

Rethinking the green power grid for stability, not just for climate

The 2025 Iberian blackout has renewed concerns about the resilience of power grids with high shares of renewable generation. This commentary argues that renewable generation can not only advance decarbonization but also strengthen grid stability through synthetic inertia, advanced inverter-based control, and coordinated transmission planning. Rapid advances in energy storage and power electronics make this transition increasingly viable.

eess.SY↗

arXiv2026

Irregular Metamaterial Networks

Metamaterials can achieve exceptional functionality through careful engineering of their mesoscale structure. Although appropriately introduced irregularities can be advantageous, current approaches largely conform to regular structures to preserve tractability. Here, we contend that network theory, enriched with geometry and physics, provides a natural framework for designing metamaterials with controlled irregularities at relevant scales, thereby enabling the discovery of new property-enhancing structures. We examine how this augmented network theory can facilitate the creation of irregular metamaterials with enhanced or novel properties and how metamaterial research, in turn, is opening new directions in network science. Supported by machine learning and advanced self-assembly, the emerging field of irregular metamaterial networks is poised to transform inverse design and scalable manufacturing of novel materials.

cond-mat.dis-nn↗

arXiv2026

Energy-Based Dynamical Models for Neurocomputation, Learning, and Optimization

Recent advances at the intersection of control theory, neuroscience, and machine learning have revealed novel mechanisms by which dynamical systems perform computation. These advances encompass a wide range of conceptual, mathematical, and computational ideas, with applications for model learning and training, memory retrieval, data-driven control, and optimization. This tutorial focuses on neuro-inspired approaches to computation that aim to improve scalability, robustness, and energy efficiency across such tasks, bridging the gap between artificial and biological systems. Particular emphasis is placed on energy-based dynamical models that encode information through gradient flows and energy landscapes. We begin by reviewing classical formulations, such as continuous-time Hopfield networks and Boltzmann machines, and then extend the framework to modern developments. These include dense associative memory models for high-capacity storage, oscillator-based networks for large-scale optimization, and proximal-descent dynamics for composite and constrained reconstruction. The tutorial demonstrates how control-theoretic principles can guide the design of next-generation neurocomputing systems, steering the discussion beyond conventional feedforward and backpropagation-based approaches to artificial intelligence.

cs.LG↗

arXiv2025

Noncooperative Quantum Networks

Existing protocols for quantum communication networks usually assume an initial allocation of quantum entanglement resources, which are then manipulated through local operations and classical communication (LOCC) to establish high-fidelity entanglement between distant parties. It is generally held that the resulting fidelity would increase monotonically with the entanglement budget. Here, we show that for noncooperative LOCC protocols, the resulting fidelity may decrease as more entanglement is added to a network with non-pure states. This effect results from a quantum analog of selfish routing and constitutes a potential obstacle to the optimal use of resources in large quantum networks.

quant-ph↗

arXiv2025

Interpretable disorder-promoted synchronization and coherence in coupled laser networks

Coupled lasers offer a promising approach to scaling the power output of photonic devices for applications demanding high frequency precision and beam coherence. However, maintaining coherence among lasers remains a fundamental challenge due to desynchronizing instabilities arising from time delay in the optical coupling. Here, we depart from the conventional notion that disorder is detrimental to synchronization and instead propose an interpretable mechanism through which heterogeneity in the laser parameters can be harnessed to promote synchronization. Our approach allows stabilization of pre-specified synchronous states that, while abundant, are often unstable in systems of identical lasers. The results show that stable synchronization enabling coherence can be frequently achieved by introducing intermediate levels of random mismatches in any of several laser constructive parameters. Our results establish a principled framework for enhancing coherence in large laser networks, offering a robust strategy for power scaling in photonic systems.

cond-mat.dis-nn↗

arXiv2025

Grid congestion stymies climate benefit from U.S. vehicle electrification

Averting catastrophic global warming requires decisive action to decarbonize key sectors. Vehicle electrification, alongside renewable energy integration, is a long-term strategy toward zero carbon emissions. However, transitioning to fully renewable electricity may take decades -- during which electric vehicles may still rely on carbon-intensive electricity. We analyze the critical role of the transmission network in enabling or constraining emissions reduction from U.S. vehicle electrification. Our models reveal that the available transmission capacity severely limits potential CO2 emissions reduction. With adequate transmission, full electrification could nearly eliminate vehicle operational CO2 emissions once renewable generation reaches the existing nonrenewable capacity. In contrast, the current grid would support only a fraction of that benefit. Achieving the full emissions reduction potential of vehicle electrification during this transition will require a moderate but targeted increase in transmission capacity. Our findings underscore the pressing need to enhance transmission infrastructure to unlock the climate benefits of large-scale electrification and renewable integration.

eess.SY↗

arXiv2025

Hybrid satellite-fiber quantum network

Quantum networks hold promise for key distribution, private and distributed computing, and quantum sensing, among other applications. The scale of such networks for ground users is currently limited by one's ability to distribute entanglement between distant locations. This can in principle be carried out by transmitting entangled photons through optical fibers or satellites. The former is limited by fiber-optic attenuation while the latter is limited by atmospheric extinction and diffraction. Here, we propose a hybrid network and protocol that outperform both ground- and satellite-based designs and lead to high-fidelity entanglement at a continental or even global scale.

quant-ph↗

arXiv2025

Introduction to Focus Issue: Topics in Nonlinear Science

Nonlinear science has evolved significantly over the 35 years since the launch of the journal Chaos. This Focus Issue, dedicated to the 80th Birthday of its founding editor-in-chief, David K. Campbell, brings together a selection of contributions on influential topics, many of which were advanced by Campbell's own research program and leadership role. The topics include new phenomena and method development in the realms of network dynamics, machine learning, quantum and material systems, chaos and fractals, localized states, and living systems, with a good balance of literature review, original contributions, and perspectives for future research.

nlin.AO↗

arXiv2025

Distributed Lyapunov Functions for Nonlinear Networks

Nonlinear networks are often multistable, exhibiting coexisting stable states with competing regions of attraction (ROAs). As a result, ROAs can have complex "tentacle-like" morphologies that are challenging to characterize analytically or computationally. In addition, the high dimensionality of the state space prohibits the automated construction of Lyapunov functions using state-of-the-art optimization methods, such as sum-of-squares (SOS) programming. In this letter, we propose a distributed approach for the construction of Lyapunov functions based solely on local information. To this end, we establish an augmented comparison lemma that characterizes the existence conditions of partial Lyapunov functions, while also accounting for residual effects caused by the associated dimensionality reduction. These theoretical results allow us to formulate an SOS optimization that iteratively constructs such partial functions, whose aggregation forms a composite Lyapunov function. The resulting composite function provides accurate convex approximations of both the volumes and shapes of the ROAs. We validate our method on networks of van der Pol and Ising oscillators, demonstrating its effectiveness in characterizing high-dimensional systems with non-convex ROAs.

eess.SY↗

arXiv2025

On the Popov-Belevitch-Hautus tests for functional observability and output controllability

Functional observability and output controllability are properties that establish the conditions for the partial estimation and partial control of the system state, respectively. In the special case of full-state observability and controllability, the Popov-Belevitch-Hautus (PBH) tests provide conditions for the properties to hold based on the system eigenspace. Generalizations of the PBH test have been recently proposed for functional observability and output controllability, but thus far have only been proven valid for diagonalizable systems. Here, we rigorously establish the generalized PBH test for functional observability, extending its validity to a broader class of systems using Jordan decomposition. Likewise, we determine the class of systems under which the generalized PBH test is sufficient and necessary for output controllability. These results have immediate implications for observer and controller design, pole assignment, and optimal placement of sensors and drivers.

math.OC↗

arXiv2025

Duality between controllability and observability for target control and estimation in networks

Output controllability and functional observability are properties that enable, respectively, the control and estimation of part of the state vector. These notions are of utmost importance in applications to high-dimensional systems, such as large-scale networks, in which only a target subset of variables (nodes) is sought to be controlled or estimated. Although the duality between full-state controllability and observability is well established, the characterization of the duality between their generalized counterparts remains an outstanding problem. Here, we establish both the weak and the strong duality between output controllability and functional observability. Specifically, we show that functional observability of a system implies output controllability of a dual system (weak duality), and that under a certain geometric condition the converse holds (strong duality). As an application of the strong duality, we derive a necessary and sufficient condition for target control via static feedback. This allow us to establish a separation principle between the design of target controllers and the design of functional observers in closed-loop systems. These results generalize the classical duality and separation principles in modern control theory.

math.OC↗

arXiv2025

Frequency Synchronization Induced by Frequency Detuning

It is widely held that identical systems tend to behave similarly under comparable conditions. Yet, for systems that interact through a network, symmetry breaking can lead to scenarios in which this expectation does not hold. Prominent examples are chimera states in multistable phase-oscillator networks. Here, we show that for a broad class of such networks, asynchronous states can be converted into frequency-synchronized states when identical oscillators are detuned to have different intrinsic frequencies. Importantly, we show that frequency synchronization is achieved over a range of intrinsic frequency detuning and is thus a robust effect. These results, which are supported by theory, simulations, and electrochemical oscillator experiments, reveal a counterintuitive opportunity to use parameter heterogeneity to promote synchronization.

nlin.PS↗

arXiv2025

Global Optimization Through Heterogeneous Oscillator Ising Machines

Oscillator Ising machines (OIMs) are networks of coupled oscillators that seek the minimum energy state of an Ising model. Since many NP-hard problems are equivalent to the minimization of an Ising Hamiltonian, OIMs have emerged as a promising computing paradigm for solving complex optimization problems that are intractable on existing digital computers. However, their performance is sensitive to the choice of tunable parameters, and convergence guarantees are mostly lacking. Here, we show that lower energy states are more likely to be stable, and that convergence to the global minimizer is often improved by introducing random heterogeneities in the regularization parameters. Our analysis relates the stability properties of Ising configurations to the spectral properties of a signed graph Laplacian. By examining the spectra of random ensembles of these graphs, we show that the probability of an equilibrium being asymptotically stable depends inversely on the value of the Ising Hamiltonian, biasing the system toward low-energy states. Our numerical results confirm our findings and demonstrate that heterogeneously designed OIMs efficiently converge to globally optimal solutions with high probability.

math.OC↗

arXiv2025

Optimal flock formation induced by agent heterogeneity

The study of flocking in biological systems has identified conditions for self-organized collective behavior, inspiring the development of decentralized strategies to coordinate the dynamics of swarms of drones and other autonomous vehicles. Previous research has focused primarily on the role of the time-varying interaction network among agents while assuming that the agents themselves are identical or nearly identical. Here, we depart from this conventional assumption to investigate how inter-individual differences between agents affect the stability and convergence in flocking dynamics. We show that flocks of agents with optimally assigned heterogeneous parameters significantly outperform their homogeneous counterparts, achieving 20-40% faster convergence to desired formations across various control tasks. These tasks include target tracking, flock formation, and obstacle maneuvering. In systems with communication delays, heterogeneity can enable convergence even when flocking is unstable for identical agents. Our results challenge existing paradigms in multi-agent control and establish system disorder as an adaptive, distributed mechanism to promote collective behavior in flocking dynamics.

cond-mat.dis-nn↗