Ming Cao

• University of Groningen

Laplacian dynamics on a signless graph characterize a class of linear interactions, where pairwise cooperative interactions between all agents lead to the convergence to a common state. On a structurally balanced signed graph, the agents converge to values of the same magnitude but opposite signs (bipartite consensus), as illustrated by the well-kn...

Combined prosocial incentives, integrating reward for cooperators and punishment for defectors, are effective tools to promote cooperation among competing agents in population games. Existing research concentrated on how to adjust reward or punishment, as two mutually exclusive tools, during the evolutionary process to achieve the desired proportio...

In graph-theoretical terms, an edge in a graph connects two vertices while a hyperedge of a hypergraph connects any more than one vertices. If the hypergraph's hyperedges further connect the same number of vertices, it is said to be uniform . In algebraic graph theory, a graph can be characterized by an adjacency matrix, and similarly, a uniform hy...

Neuromorphic computing is an interdisciplinary field that combines principles of computer engineering, electronics, and neuroscience, aiming to design hardware and software that can process information in a similar manner to biological brains, offering advantages in efficiency, adaptability, and cognitive capabilities. In this work, we propose a co...

This paper studies observability for non-uniform hypergraphs with inputs and outputs. To capture higher-order interactions, we define a canonical non-homogeneous dynamical system with nonlinear outputs on hypergraphs. We then construct algebraic necessary and sufficient conditions based on polynomial ideals and varieties for global observability at...

It is known that the effect of species' density on species' growth is non-additive in real ecological systems. This challenges the conventional Lotka-Volterra model, where the interactions are always pairwise and their effects are additive. To address this challenge, we introduce HOIs (Higher-Order Interactions) which are able to capture, for examp...

We study a prototypical non-polynomial decision-making model for which agents in a population potentially alternate between two consumption strategies, one related to the exploitation of an unlimited but considerably expensive resource and the other a comparably cheaper but restricted and slowly renewable source. In particular, we study a model fol...

We design a distributed coordinated guiding vector field (CGVF) for a group of robots to achieve ordering-flexible motion coordination while maneuvering on a desired two-dimensional (2D) surface. The CGVF is characterized by three terms, i.e., a convergence term to drive the robots to converge to the desired surface, a propagation term to provide a...

In graph-theoretical terms, an edge in a graph connects two vertices while a hyperedge of a hypergraph connects any more than one vertices. If the hypergraph's hyperedges further connect the same number of vertices, it is said to be uniform. In algebraic graph theory, a graph can be characterized by an adjacency matrix, and similarly, a uniform hyp...

This paper studies the stability of discrete-time polynomial dynamical systems on hypergraphs by utilizing the Perron–Frobenius theorem for nonnegative tensors with respect to the tensors’ Z-eigenvalues and Z-eigenvectors. Firstly, for a multilinear polynomial system on a uniform hypergraph, we study the stability of the origin of the corresponding...

This paper tightens the classical Poincaré–Bendixson theory for a positively invariant, simply-connected compact set M in a continuously differentiable planar vector field by further characterizing for any point p ∈ M , the composition of the limit sets ω ( p ) and α ( p ) after counting separately the fixed points on M 's boundary and interior. In...

Empirical studies suggest a deep intertwining between opinion formation and decision-making processes, but these have been treated as separate problems in the study of dynamical models for social networks. In this paper, we bridge the gap in the literature by proposing a novel coevolutionary model, in which each individual selects an action from a...

Over the past decades, chimera states have attracted considerable attention given their unexpected symmetry-breaking spatiotemporal nature and simultaneously exhibiting synchronous and incoherent behaviors under specific conditions. Despite relevant precursory results of such unforeseen states for diverse physical and topological configurations, th...

In the vector-field guided path-following problem, a sufficiently smooth vector field is designed such that its integral curves converge to and move along a one-dimensional geometric desired path. The existence of singular points where the vector field vanishes creates a topological obstruction to global convergence to the desired path and some ass...

Motivated by massive outbreaks of COVID-19 that occurred even in populations with high vaccine uptake, we propose a novel multi-population temporal network model for the spread of recurrent epidemic diseases. We study the effect of human behavior, testing, and vaccination campaigns on infection prevalence and local outbreak control. Our modeling fr...

Seals are well‐known for their remarkable hydrodynamic trail‐following capabilities made possible by undulating flow‐sensing whiskers that enable the seals to detect fish swimming as far as 180 m away. In this work, the form‐function relationship in the undulating whiskers of two different phocid seal species, viz. harbor and gray seals, is studied...

While conventional graphs only characterize pairwise interactions, higher-order networks (hypergraph, simplicial complex) capture multi-body interactions, which is a potentially more suitable modeling framework for a complex real system. However, the introduction of higher-order interactions brings new challenges for the rigorous analysis of such s...

Wavy Whiskers in Wakes It is known that seals can detect prey up to 180 m away using their flow‐sensing whiskers, which feature undulating morphologies that reduce vortex‐induced vibrations. In article number 2203062 by Xingwen Zheng, Ajay Giri Prakash Kottapalli, and co‐workers, through fluid‐structure interaction studies and experimental investig...

Microscopic strategy update rules play an important role in the evolutionary dynamics of cooperation among interacting agents on complex networks. Many previous related works only consider one fixed rule, while in the real world, individuals may switch, sometimes periodically, between rules. It is of particular theoretical interest to investigate...

Imitation is widely observed in populations of decision-making agents. Using our recent convergence results for asynchronous imitation dynamics on networks, we consider how such networks can be efficiently driven to a desired equilibrium state by offering payoff incentives for using a certain strategy, either uniformly or targeted to individuals. I...

Seals can detect prey up to 180 m away using only their flow‐sensing whiskers. The unique undulating morphology of Phocid seal whiskers reduces vortex‐induced vibrations (VIVs), rendering seals highly sensitive to biologically relevant flow stimuli. In this work, digital models of harbor and grey seal whiskers are extracted using 3D scanning and a...

Motivated by the climate crisis that is currently ravaging the planet, we propose and analyze a novel framework for the evolution of anthropogenic climate impact in which the evolution of human environmental behavior and environmental impact is coupled. Our framework includes a human decision-making process that captures social influence, governmen...

Underwater Sensing Seals can detect prey up to 180 m away using their flow‐sensing whiskers, which feature undulating morphologies that reduce vortex‐induced vibrations. In article number 2207274, Ajay Giri Prakash Kottapalli, Xingwen Zheng, and co‐workers investigate harbor and grey seal whiskers' interactions with the flow and find that neighbori...

Recently, an evolutionary game dynamics model taking into account the environmental feedback has been proposed to describe the co-evolution of strategic actions of a population of individuals and the state of the surrounding environment; correspondingly a range of interesting dynamic behaviors have been reported. In this paper, we provide new theor...

Biophysical models of large-scale brain activity are a fundamental tool for understanding the mechanisms underlying the patterns observed with neuroimaging. These models combine a macroscopic description of the within- and between-ensemble dynamics of neurons within a single architecture. A challenge for these models is accounting for modulations o...

Dynamic norms have recently emerged as a powerful method to encourage individuals to adopt an innovation by highlighting a growing trend in its uptake. However, there have been no concrete attempts to understand how this individual-level mechanism might shape the collective population behavior. Here, we develop a framework to examine this by encaps...

We propose coordinating guiding vector fields to achieve two tasks simultaneously with a team of robots: first, the guidance and navigation of multiple robots to possibly different paths or surfaces typically embedded in 2D or 3D; second, their motion coordination while tracking their prescribed paths or surfaces. The motion coordination is defined...

Motivated by massive outbreaks of COVID-19 that occurred even in populations with high vaccine uptake, we propose a novel multi-population temporal network model for the spread of recurrent epidemic diseases. We study the effect of human behavior, testing, and vaccination campaigns on the control of local outbreaks and infection prevalence. Our mod...

This article studies 2-D formation stabilization and maneuvering of mobile agents governed by double-integrator dynamics. The desired formation is described by a set of triple-agent interior angles. A carefully chosen such set of angle constraints guarantees that the desired formation is angle rigid. To achieve the desired angle rigid formation, a...

In this paper, we show that the domain of attraction of a compact asymptotically stable submanifold in a finite-dimensional smooth manifold of an autonomous system is homeomorphic to the submanifold’s tubular neighborhood. The compactness of the submanifold is crucial, without which this result is false; two counterexamples are provided to demonstr...

Many marine animals perform fascinating survival hydrodynamics and perceive their surroundings through optimally evolved sensory systems. For instance, phocid seal whiskers have undulations that allow them to resist noisy self‐induced vortex‐induced vibrations (VIV) while locking their vibration frequencies to wakes generated by swimming fishes. In...

Accurately following a geometric desired path in a two-dimensional (2-D) space is a fundamental task for many engineering systems, in particular mobile robots. When the desired path is occluded by obstacles, it is necessary and crucial to temporarily deviate from the path for obstacle/collision avoidance. In this article, we develop a composite gui...

This paper studies a discrete-time time-varying multi-layer networked SIWS (susceptible-infected-water-susceptible) model with multiple resources under both single-virus and competing multi-virus settings. Besides the human-to-human interaction, we also consider that the disease can diffuse on different types of medium. We use \emph{resources} to r...

Modeling opinion formation and decision-making processes, important in their own rights, have been treated as separate problems in the study of dynamical models for social networks. Empirical studies suggest a deep intertwining between these two processes, and in this paper, we bridge the gap in the existing research by proposing a novel coevolutio...

Accurately following a geometric desired path in a two-dimensional space is a fundamental task for many engineering systems, in particular mobile robots. When the desired path is occluded by obstacles, it is necessary and crucial to temporarily deviate from the path for obstacle/collision avoidance. In this paper, we develop a composite guiding vec...

Recently, an evolutionary game dynamics model taking into account the environmental feedback has been proposed to describe the co-evolution of strategic actions of a population of individuals and the state of the surrounding environment; correspondingly a range of interesting dynamic behaviors have been reported. In this paper, we provide new theor...

Imitation is widely observed in nature and often used to model populations of decision-making agents, but it is not yet known under what conditions a network of imitators will reach a state where they are satisfied with their decisions. We show that every network in which agents imitate the best performing strategy in their neighborhood will reach...

Performing a cognitive task requires going through a sequence of functionally diverse stages. Although it is typically assumed that these stages are characterized by distinct states of cortical synchrony that are triggered by sub-cortical events, little reported evidence supports this hypothesis. To test this hypothesis, we first identified cogniti...

A path-following control algorithm enables a system's trajectories under its guidance to converge to and evolve along a given geometric desired path. There exist various such algorithms, but many of them can only guarantee local convergence to the desired path in its neighborhood. In contrast, the control algorithms using a well-designed guiding ve...

In this paper, we show that the domain of attraction of a compact asymptotically stable submanifold of a finite-dimensional smooth manifold of an autonomous system is homeomorphic to its tubular neighborhood. The compactness of the attractor is crucial, without which this result is false; two counterexamples are provided to demonstrate this.

A path-following control algorithm enables a system's trajectories to converge to and evolve along a given geometric desired path. There exist various such algorithms, but many of them can only guarantee local convergence to the desired path in its neighborhood. In contrast, the control algorithms using a well-designed guiding vector field can ensu...

The spread of an epidemic disease and the population's collective behavioral response are deeply intertwined, influencing each other's evolution. Such a co-evolution typically has been overlooked in mathematical models, limiting their real-world applicability. To address this gap, we propose and analyse a behavioral-epidemic model, in which a susce...

In this article, we propose coordinating guiding vector fields to achieve two tasks simultaneously with a team of robots: first, the guidance and navigation of multiple robots to possibly different paths or surfaces typically embedded in 2-D or 3-D, and second, their motion coordination while tracking their prescribed paths or surfaces. The motion...

In this article, we propose a stochastic network model for the spread of common sexually transmitted infections (STIs). The model expands the standard susceptible–infected–susceptible model by incorporating asymptomatic infected individuals—who are unaware that they are posing a health threat to themselves and the population—and individuals' behavi...

Motivated by the increasing number of COVID-19 cases that have been observed in many countries after the vaccination and relaxation of non-pharmaceutical interventions, we propose a mathematical model on time-varying networks for the spread of recurrent epidemic diseases in a partially vaccinated population. The model encapsulates several realistic...

The environment around general-purpose service robots has a dynamic nature. Accordingly, even the robot's programmer cannot predict all the possible external failures which the robot may confront. This research proposes an online incremental learning method that can be further used to autonomously handle external failures originating from a change...

Seals are known to use their highly sensitive whiskers to precisely follow the hydrodynamic trail left behind by prey. Studies estimate that a seal can track a herring that is swimming as far as 180 m away, indicating an incredible detection apparatus on a par with the echolocation system of dolphins and porpoises. This remarkable sensing capabilit...

This letter presents some new criteria for partial exponential stability of a slow-fast nonlinear system with a fast scalar variable using periodic averaging methods. Unlike classical averaging techniques, we construct an averaged system by averaging over this fast scalar variable instead of the time variable. We show that partial exponential stabi...

Social conventions change when individuals collectively adopt an alternative over the status quo, in a process known as social diffusion. Our repeated trials of a multi-round experiment provided data that helped motivate the proposal of an agent-based model of social diffusion that incorporates inertia and trend-seeking, two behavioural mechanisms...

Understanding how to effectively control an epidemic spreading on a network is a problem of paramount importance for the scientific community. The ongoing COVID-19 pandemic has highlighted the need for policies that mitigate the spread, without relying on pharmaceutical interventions, that is, without the medical assurance of the recovery process....

Performing a cognitive task requires going through a sequence of functionally diverse stages. Although it is typically assumed that these stages are characterized by distinct states of cortical synchrony that are triggered by sub-cortical events, little reported evidence supports this hypothesis. To test this hypothesis, we first identified cogniti...

The spreading dynamics of an epidemic and the collective behavioral pattern of the population over which it spreads are deeply intertwined and the latter can critically shape the outcome of the former. Motivated by this, we design a parsimonious game-theoretic behavioral-epidemic model, in which an interplay of realistic factors shapes the coevolut...

In robot navigation tasks, such as unmanned aerial vehicle (UAV) highway traffic monitoring, it is important for a mobile robot to follow a specified desired path. However, most of the existing path-following navigation algorithms cannot guarantee global convergence to desired paths or enable following self-intersected desired paths due to the exis...

The fast-slow dynamics of eco-evolutionary systems are studied, where we consider the feedback actions of environmental resources that are classified into those that are self-renewing and those externally supplied. We show that although these two types of resources are drastically different, the resulting closed-loop systems bear close resemblances...

In privacy-preserving controller design, there is usually a trade-off between the privacy level and control performances, and we show in this paper that this trade-off in particular determines a lower bound on the differential privacy level of the closed-loop system. The control task we consider is reference tracking in a plug-and-play setting, and...

It is essential in many applications to impose a scalable coordinated motion control on a large group of mobile robots, which is efficient in tasks requiring repetitive execution, such as environmental monitoring. In this paper, we design a guiding vector field to guide multiple robots to follow possibly different desired paths while coordinating t...

This paper investigates how to maneuver a planar formation of mobile agents using designed mismatched angles. The desired formation shape is specified by a set of interior angle constraints. To realize the maneuver of translation, rotation and scaling of the formation as a whole, we intentionally force the agents to maintain mismatched desired angl...

In both economic and evolutionary theories of games, two general classes of evolution can be identified: 1) dynamics based on myopic optimization and 2) dynamics based on imitations or replications. The collective behavior of structured populations governed by these dynamics can vary significantly. Particularly in social dilemmas, myopic optimizati...

This paper focuses on properties of equilibria and their associated regions of attraction for continuous-time nonlinear dynamical systems. The classical Poincar\'e--Hopf Theorem is used to derive a general result providing a sufficient condition for the system to have a unique equilibrium. The condition involves the Jacobian of the system at possib...

A biochemical oscillator model, describing developmental stage of myxobacteria, is analyzed mathematically. Observations from numerical simulations show that in a certain range of parameters, the corresponding system of ordinary differential equations displays stable and robust oscillations. In this work, we use geometric singular perturbation theo...

During the ongoing COVID-19 pandemic, mathematical models of epidemic spreading have emerged as powerful tools to produce valuable predictions of the evolution of the pandemic, helping public health authorities decide which intervention policies should be implemented. The study of these models -- grounded in the systems theory and often analyzed us...

Partial, instead of complete, synchronization has been widely observed in various networks including, in particular, brain networks. Motivated by data from human brain functional networks, in this technical note, we analytically show that partial synchronization can be induced by strong regional connections in coupled subnetworks of Kuramoto oscill...

Situations in which immediate self-interest and long-term collective interest conflict often require some form of influence to prevent them from leading to undesirable or unsustainable outcomes. Next to sanctioning, social influence and social structure, it is possible that strategic solutions can exist for these social dilemmas. However, the exist...

Synchrony of neuronal ensembles is believed to facilitate information exchange among cortical regions in the human brain. Recently, it has been observed that distant brain areas which are not directly connected by neural links also experience synchronization. Such synchronization between remote regions is sometimes due to the presence of a mediatin...

In this paper, we study how to alleviate highway traffic congestions by encouraging plug-in electric and hybrid vehicles to stop at charging stations around peak congestion times. Specifically, we focus on a case study and simulate the adoption of a dynamic charging price depending on the traffic congestion. We use real traffic data of the A13 high...

Motivated by the literature on opinion dynamics and evolutionary game theory, we propose a novel mathematical framework to model the intertwined coevolution of opinions and decision-making in a complex social system. In the proposed framework, the members of a social community update their opinions and revise their actions as they learn of others'...

In this paper, we study how to alleviate highway traffic congestion by encouraging plug-in hybrid and electric vehicles to stop at a charging station around peak congestion times. Specifically, we design a pricing policy to make the charging price dynamic and dependent on the traffic congestion, predicted via the cell transmission model, and the av...

Biophysical models of large-scale brain activity are a fundamental tool for understanding the mechanisms underlying the patterns observed with neuroimaging. These models combine a macroscopic description of the within- and between-ensemble dynamics of neurons within a single architecture. A challenge for these models is accounting for modulations o...

Most of the existing path-following navigation algorithms cannot guarantee global convergence to desired paths or enable following self-intersected desired paths due to the existence of singular points where navigation algorithms return unreliable or even no solutions. One typical example arises in vector-field guided path-following (VF-PF) navigat...

In this article, we study the problem of affine formation stabilization for multiagent systems in the plane. The challenges lie in the limited access to the information of the target formation in the sense that the prescribed values of the formation parameters, that is, the scaling size and rotation angle, are known only by one agent which we call...

In two-player repeated games, Zero-Determinant (ZD) strategies enable a player to unilaterally enforce a linear payoff relation between her own and her opponent's payoff irrespective of the opponent's strategy. This manipulative nature of the ZD strategies attracted significant attention from researchers due to its close connection to controlling d...

This paper analyzes a nonlinear opinion dynamics model which generalizes the DeGroot model by introducing a bias parameter for each individual. The original DeGroot model is recovered when the bias parameter is equal to zero. The magnitude of this parameter reflects an individual’s degree of bias when assimilating new opinions, and depending on the...

A multi-agent system designed to achieve distance-based shape control with flocking behavior can be seen as a mechanical system described by a Lagrangian function and subject to additional external forces. Forced variational integrators are given by the discretization of Lagrange-d'Alembert principle for systems subject to external forces, and have...

Motivated by the challenging formation stabilization problem for mobile robotic teams wherein no distance or relative position measurements are available but each robot can only measure some of relative angles with respect to its neighbors in its local coordinate frame, we develop the notion of "angle rigidity" for a multi-point framework, named "a...

We study the distributed model predictive control (DMPC) problem for a network of linear discrete-time systems, where the system dynamics are decoupled, the system constraints are coupled, and the communication networks are described by time-varying directed graphs. A novel distributed optimization algorithm called the push-sum dual gradient (PSDG)...

Linear threshold models have been studied extensively in structured populations; however, less attention is paid to perception differences among the individuals of the population. To focus on this effect, we exclude structure and consider a well-mixed population of heterogeneous agents, each associated with a threshold in the form of a fixed ratio...

During the course of an epidemic, individuals constantly make decisions on how to fight against epidemic spreading. Collectively, these individual decisions are critical to the global outcome of the epidemic, especially when no pharmaceutical interventions are available. However, existing epidemic models lack the ability to capture this complex dec...

Motivated by the literature on opinion dynamics and evolutionary game theory, we propose a novel mathematical framework to model the intertwined coevolution of opinions and decision-making in a complex social system. In the proposed framework, the members of a social community update their opinions and revise their actions as they learn of others’...

In this paper, we present three distributed algorithms to solve a class of Generalized Nash Equilibrium (GNE) seeking problems in strongly monotone games. The first one (SD-GENO) is based on synchronous updates of the agents, while the second and the third (AD-GEED and AD-GENO) represent asynchronous solutions that are robust to communication delay...

In this paper, we study proximal type dynamics in the context of multi-agent network games. We analyze several conjugations of this class of games, providing convergence results. Specifically, we look into synchronous/asynchronous dynamics with time-invariant communication network and synchronous dynamics with time-varying communication networks. F...

Many of today’s most pressing societal concerns require decisions which take into account a distant and uncertain future. Recent developments in strategic decision-making suggest that individuals, or a small group of individuals, can unilaterally influence the collective outcome of such complex social dilemmas. However, these results do not account...

Using a designed vector field to control a mobile robot to follow a given desired path has found a range of practical applications, and it is in great need to further build a rigorous theory to guide its implementation. In this paper, we study the properties of a general 3D vector field for robotic path following. We stipulate and investigate assum...