An official website of the United States government
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. 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.
more »
« less
This content will become publicly available on November 27, 2025
Coordinated behavior of autonomous microscopic machines through local electronic pulse coupling
Increasingly functional microscopic machines are poised to have massive technical influence in areas including targeted drug delivery, precise surgical interventions, and environmental remediation. Such functionalities would increase markedly if collections of these microscopic machines were able to coordinate their function to achieve cooperative emergent behaviors. Implementing such coordination, however, requires a scalable strategy for synchronization—a key stumbling block for achieving collective behaviors of multiple autonomous microscopic units. Here, we show that pulse-coupled complementary metal-oxide semiconductor oscillators offer a tangible solution for such scalable synchronization. Specifically, we designed low-power oscillating modules with attached mechanical elements that exchange electronic pulses to advance their neighbor’s phase until the entire system is synchronized with the fastest oscillator or “leader.” We showed that this strategy is amenable to different oscillator connection topologies. The cooperative behaviors were robust to disturbances that scrambled the synchronization. In addition, when connections between oscillators were severed, the resulting subgroups synchronized on their own. This advance opens the door to functionalities in microscopic robot swarms that were once considered out of reach, ranging from autonomously induced fluidic transport to drive chemical reactions to cooperative building of physical structures at the microscale.
more »
« less
- PAR ID:
- 10590695
- Publisher / Repository:
- Science Journals AAAS
- Date Published:
- Journal Name:
- Science Robotics
- Volume:
- 9
- Issue:
- 96
- ISSN:
- 2470-9476
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
In this paper we study cluster synchronization in a network of Kuramoto oscillators, where groups of oscillators evolve cohesively and at different frequencies from the neigh- boring oscillators. Synchronization is critical in a variety of systems, where it enables complex functionalities and behaviors. Synchronization over networks depends on the oscillators’ dynamics, the interaction topology, and coupling strengths, and the relationship between these different factors can be quite intricate. In this work we formally show that three network properties enable the emergence of cluster synchronization. Specifically, weak inter-cluster connections, strong intra-cluster connections, and sufficiently diverse natural frequencies among oscillators belonging to different groups. Our approach relies on system-theoretic tools, and is validated with numerical studies.more » « less
-
We investigate the entrainment of electrochemical oscillators with different phase response curves (PRCs) using a global signal: the goal is to achieve the desired phase configuration using a minimum-power waveform. Establishing the desired phase relationships in a highly nonlinear networked system exhibiting significant heterogeneities, such as different conditions or parameters for the oscillators, presents a considerable challenge because different units respond differently to the common global entraining signal. In this work, we apply an optimal phase-selective entrainment technique in both a kinetic model and experiments involving electrochemical oscillators in achieving phase synchronized states. We estimate the PRCs of the oscillators at different circuit potentials and external resistance, and entrain pairs and small sets of four oscillators in various phase configurations. We show that for small PRC variations, phase assignment can be achieved using an averaged PRC in the control design. However, when the PRCs are sufficiently different, individual PRCs are needed to entrain the system with the expected phase relationships. The results show that oscillator assemblies with heterogeneous PRCs can be effectively entrained to desired phase configurations in practical settings. These findings open new avenues to applications in biological and engineered oscillator systems where synchronization patterns are essential for system performance.more » « less
-
Abstract Spontaneous synchronization is ubiquitous in natural and man-made systems. It underlies emergent behaviors such as neuronal response modulation and is fundamental to the coordination of robot swarms and autonomous vehicle fleets. Due to its simplicity and physical interpretability, pulse-coupled oscillators has emerged as one of the standard models for synchronization. However, existing analytical results for this model assume ideal conditions, including homogeneous oscillator frequencies and negligible coupling delays, as well as strict requirements on the initial phase distribution and the network topology. Using reinforcement learning, we obtain an optimal pulse-interaction mechanism (encoded in phase response function) that optimizes the probability of synchronization even in the presence of nonideal conditions. For small oscillator heterogeneities and propagation delays, we propose a heuristic formula for highly effective phase response functions that can be applied to general networks and unrestricted initial phase distributions. This allows us to bypass the need to relearn the phase response function for every new network.more » « less
-
Abstract The striking similarity between biological locomotion gaits and the evolution of phase patterns in coupled oscillatory network can be traced to the role of central pattern generator located in the spinal cord. Bio-inspired robotics aim at harnessing this control approach for generation of rhythmic patterns for synchronized limb movement. Here, we utilize the phenomenon of synchronization and emergent spatiotemporal pattern from the interaction among coupled oscillators to generate a range of locomotion gait patterns. We experimentally demonstrate a central pattern generator network using capacitively coupled Vanadium Dioxide nano-oscillators. The coupled oscillators exhibit stable limit-cycle oscillations and tunable natural frequencies for real-time programmability of phase-pattern. The ultra-compact 1 Transistor-1 Resistor implementation of oscillator and bidirectional capacitive coupling allow small footprint area and low operating power. Compared to biomimetic CMOS based neuron and synapse models, our design simplifies on-chip implementation and real-time tunability by reducing the number of control parameters.more » « less
