First, studying persistent currents in confined chaotic Dirac fermion systems with a ring geometry and an applied Aharonov-Bohm flux, unusual whispering-gallery modes with edge-dependent currents and spin polarization are identified. They can survive for highly asymmetric rings that host fully developed classical chaos. By sustaining robust persistent currents, these modes can be utilized to form a robust relativistic quantum two-level system.
Second, the quantized topological edge states in confined massive Dirac fermion systems exhibiting a remarkable reverse Stark effect in response to an applied electric field, and an electrically or optically controllable spin switching behavior are uncovered.
Third, novel wave scattering and transport in Dirac-like pseudospin-1 systems are reported. (a), for small scatterer size, a surprising revival resonant scattering with a peculiar boundary trapping by forming unusual vortices is uncovered. Intriguingly, it can persist in arbitrarily weak scatterer strength regime, which underlies a superscattering behavior beyond the conventional scenario. (b), for larger size, a perfect caustic phenomenon arises as a manifestation of the super-Klein tunneling effect. (c), in the far-field, an unexpected isotropic transport emerges at low energies.
Fourth, a geometric valley Hall effect (gVHE) originated from fractional singular Berry flux is revealed. It is shown that gVHE possesses a nonlinear dependence on the Berry flux with asymmetrical resonance features and can be considerably enhanced by electrically controllable resonant valley skew scattering. With the gVHE, efficient valley filtering can arise and these phenomena are robust against thermal fluctuations and disorder averaging.
My research mainly concentrates on predicting and controlling tipping points (saddle-node bifurcation) in complex ecological systems, comparing linear and nonlinear control methods in complex dynamical systems. Moreover, I use advanced artificial neural networks to predict chaotic spatiotemporal dynamical systems. Complex networked systems can exhibit a tipping point (a “point of no return”) at which a total collapse occurs. Using complex mutualistic networks in ecology as a prototype class of systems, I carry out a dimension reduction process to arrive at an effective two-dimensional (2D) system with the two dynamical variables corresponding to the average pollinator and plant abundances, respectively. I demonstrate that, using 59 empirical mutualistic networks extracted from real data, our 2D model can accurately predict the occurrence of a tipping point even in the presence of stochastic disturbances. I also develop an ecologically feasible strategy to manage/control the tipping point by maintaining the abundance of a particular pollinator species at a constant level, which essentially removes the hysteresis associated with tipping points.
Besides, I also find that the nodal importance ranking for nonlinear and linear control exhibits opposite trends: for the former, large degree nodes are more important but for the latter, the importance scale is tilted towards the small-degree nodes, suggesting strongly irrelevance of linear controllability to these systems. Focusing on a class of recurrent neural networks - reservoir computing systems that have recently been exploited for model-free prediction of nonlinear dynamical systems, I uncover a surprising phenomenon: the emergence of an interval in the spectral radius of the neural network in which the prediction error is minimized.
Extreme events, a type of collective behavior in complex networked dynamical systems, often can have catastrophic consequences. To develop effective strategies to control extreme events is of fundamental importance and practical interest. Utilizing transportation dynamics on complex networks as a prototypical setting, we find that making the network “mobile” can effectively suppress extreme events. A striking, resonance-like phenomenon is uncovered, where an optimal degree of mobility exists for which the probability of extreme events is minimized. We derive an analytic theory to understand the mechanism of control at a detailed and quantitative level, and validate the theory numerically. Implications of our finding to current areas such as cybersecurity are discussed.
The objective of articulating sustainability visions through modeling is to enhance the outcomes and process of visioning in order to successfully move the system toward a desired state. Models emphasize approaches to develop visions that are viable and resilient and are crafted to adhere to sustainability principles. This approach is largely assembled from visioning processes (resulting in descriptions of desirable future states generated from stakeholder values and preferences) and participatory modeling processes (resulting in systems-based representations of future states co-produced by experts and stakeholders). Vision modeling is distinct from normative scenarios and backcasting processes in that the structure and function of the future desirable state is explicitly articulated as a systems model. Crafting, representing and evaluating the future desirable state as a systems model in participatory settings is intended to support compliance with sustainability visioning quality criteria (visionary, sustainable, systemic, coherent, plausible, tangible, relevant, nuanced, motivational and shared) in order to develop rigorous and operationalizable visions. We provide two empirical examples to demonstrate the incorporation of vision modeling in research practice and education settings. In both settings, vision modeling was used to develop, represent, simulate and evaluate future desirable states. This allowed participants to better identify, explore and scrutinize sustainability solutions.
We develop a completely data-driven approach to reconstructing coupled neuronal networks that contain a small subset of chaotic neurons. Such chaotic elements can be the result of parameter shift in their individual dynamical systems and may lead to abnormal functions of the network. To accurately identify the chaotic neurons may thus be necessary and important, for example, applying appropriate controls to bring the network to a normal state. However, due to couplings among the nodes, the measured time series, even from non-chaotic neurons, would appear random, rendering inapplicable traditional nonlinear time-series analysis, such as the delay-coordinate embedding method, which yields information about the global dynamics of the entire network. Our method is based on compressive sensing. In particular, we demonstrate that identifying chaotic elements can be formulated as a general problem of reconstructing the nodal dynamical systems, network connections and all coupling functions, as well as their weights. The working and efficiency of the method are illustrated by using networks of non-identical FitzHugh–Nagumo neurons with randomly-distributed coupling weights.
It has become common for sustainability science and resilience theory to be considered as complementary approaches. Occasionally the terms have been used interchangeably. Although these two approaches share some working principles and objectives, they also are based on some distinct assumptions about the operation of systems and how we can best guide these systems into the future. Each approach would benefit from some scholars keeping sustainability science and resilience theory separate and focusing on further developing their distinctiveness and other scholars continuing to explore them in combination. Three areas of research in which following different procedures might be beneficial are whether to prioritize outcomes or system dynamics, how best to take advantage of community input, and increasing the use of knowledge of the past as a laboratory for potential innovations.
The context in which many self-governed commons systems operate will likely be significantly altered as globalization processes play out over the next few decades. Such dramatic changes will induce some systems to fail and subsequently to be transformed, rather than merely adapt. Despite this possibility, research on globalization-induced transformations of social-ecological systems (SESs) is still underdeveloped. We seek to help fill this gap by exploring some patterns of transformation in SESs and the question of what factors help explain the persistence of cooperation in the use of common-pool resources through transformative change. Through the analysis of 89 forest commons in South Korea that experienced such transformations, we found that there are two broad types of transformation, cooperative and noncooperative. We also found that two system-level properties, transaction costs associated group size and network diversity, may affect the direction of transformation. SESs with smaller group sizes and higher network diversity may better organize cooperative transformations when the existing system becomes untenable.
The relation between flux and fluctuation is fundamental to complex physical systems that support and transport flows. A recently obtained law predicts monotonous enhancement of fluctuation as the average flux is increased, which in principle is valid but only for large systems. For realistic complex systems of small sizes, this law breaks down when both the average flux and fluctuation become large. Here we demonstrate the failure of this law in small systems using real data and model complex networked systems, derive analytically a modified flux-fluctuation law, and validate it through computations of a large number of complex networked systems. Our law is more general in that its predictions agree with numerics and it reduces naturally to the previous law in the limit of large system size, leading to new insights into the flow dynamics in small-size complex systems with significant implications for the statistical and scaling behaviors of small systems, a topic of great recent interest.
We develop a general framework to analyze the controllability of multiplex networks using multiple-relation networks and multiple-layer networks with interlayer couplings as two classes of prototypical systems. In the former, networks associated with different physical variables share the same set of nodes and in the latter, diffusion processes take place. We find that, for a multiple-relation network, a layer exists that dominantly determines the controllability of the whole network and, for a multiple-layer network, a small fraction of the interconnections can enhance the controllability remarkably. Our theory is generally applicable to other types of multiplex networks as well, leading to significant insights into the control of complex network systems with diverse structures and interacting patterns.