Rate-induced tipping in complex high-dimensional ecological networks.

In an ecosystem, environmental changes as a result of natural and human processes can cause some key parameters of the system to change with time. Depending on how fast such a parameter changes, a tipping point can occur. Existing works on rate-induced tipping, or R-tipping, offered a theoretical way to study this phenomenon but from a local dynamical point of view, revealing, e.g., the existence of a critical rate for some specific initial condition above which a tipping point will occur. As ecosystems are subject to constant disturbances and can drift away from their equilibrium point, it is necessary to study R-tipping from a global perspective in terms of the initial conditions in the entire relevant phase space region. In particular, we introduce the notion of the probability of R-tipping defined for initial conditions taken from the whole relevant phase space. Using a number of real-world, complex mutualistic networks as a paradigm, we find a scaling law between this probability and the rate of parameter change and provide a geometric theory to explain the law. The real-world implication is that even a slow parameter change can lead to a system collapse with catastrophic consequences. In fact, to mitigate the environmental changes by merely slowing down the parameter drift may not always be effective: Only when the rate of parameter change is reduced to practically zero would the tipping be avoided. Our global dynamics approach offers a more complete and physically meaningful way to understand the important phenomenon of R-tipping.

Contagion dynamics in time-varying metapopulation networks with node's activity and attractiveness.

The metapopulation network model is a mathematical framework used to study the spatial spread of epidemics with individuals' mobility. In this paper, we develop a time-varying network model in which the activity of a population is correlated with its attractiveness in mobility. By studying the spreading dynamics of the SIR (susceptible-infectious-recovered)-type disease in different correlated networks based on the proposed model, we theoretically derive the mobility threshold and numerically observe that increasing the correction between activity and attractiveness results in a reduced mobility threshold but suppresses the fraction of infected subpopulations. It also introduces greater heterogeneity in the spatial distribution of infected individuals. Additionally, we investigate the impact of nonpharmaceutical interventions on the spread of epidemics in different correlation networks. Our results show that the simultaneous implementation of self-isolation and self-protection is more effective in negatively correlated networks than that in positively correlated or non-correlated networks. Both self-isolation and self-protection strategies enhance the mobility threshold and, thus, slow down the spread of the epidemic. However, the effectiveness of each strategy in reducing the fraction of infected subpopulations varies in different correlated networks. Self-protection is more effective in positively correlated networks, whereas self-isolation is more effective in negatively correlated networks. Our study will provide insights into epidemic prevention and control in large-scale time-varying metapopulation networks.

Multistability in the cyclic competition system.

Cyclically competition models have been successful to gain an insight of biodiversity mechanism in ecosystems. There are, however, still limitations to elucidate complex phenomena arising in real competition. In this paper, we report that a multistability occurs in a simple rock-paper-scissor cyclically competition model by assuming that intraspecific competition depends on the logistic growth of each species density. This complex stability is absent in any cyclically competition model, and we investigate how the proposed intraspecific competition affects biodiversity in the existing society of three species through macroscopic and microscopic approaches. When the system is multistable, we show basins of the asymptotically stable heteroclinic cycle and stable attractors to demonstrate how the survival state is determined by initial densities of three species. Also, we find that the multistability is associated with a subcritical Hopf bifurcation. This surprising finding will give an opportunity to interpret rich dynamical phenomena in ecosystems which may occur in cyclic competition systems with different types of interactions.

Transient behavior between multi-cell flow states in ferrofluidic Taylor-Couette flow.

We investigate transient behaviors induced by magnetic fields on the dynamics of the flow of a ferrofluid in the gap between two concentric, independently rotating cylinders. Without applying any magnetic fields, we uncover emergence of flow states constituted by a combination of a localized spiral state in the top and bottom of the annulus and different multi-cell flow states with toroidally closed vortices in the interior of the bulk. However, when a magnetic field is presented, we observe the transient behaviors between multi-cell states passing through two critical thresholds in a strength of an axial (transverse) magnetic field. Before the first critical threshold of a magnetic field strength, multi-stable states with different number of cells could be observed. After the first critical threshold, we find the transient behavior between the three- and two-cell flow states. For more strength of magnetic field or after the second critical threshold, we discover that multi-cell states are disappeared and a localized spiral state remains to be stimulated. The studied transient behavior could be understood by the investigation of various quantities including a modal kinetic energy, a mode amplitude of the radial velocity, wavenumber, angular momentum, and torque. In addition, the emergence of new flow states and the transient behavior between their states in ferrofluidic flows indicate that richer and potentially controllable dynamics through magnetic fields could be possible in ferrofluic flow.

Numerical prediction of algae cell mixing feature in raceway ponds using particle tracing methods.

In the present study, a novel technique, which involves numerical computation of the mixing length of algae particles in raceway ponds, was used to evaluate the mixing process. A value of mixing length that is higher than the maximum streamwise distance (MSD) of algae cells indicates that the cells experienced an adequate turbulent mixing in the pond. A coupling methodology was adapted to map the pulsating effects of a 2D paddle wheel on a 3D raceway pond in this study. The turbulent mixing was examined based on the computations of mixing length, residence time, and algae cell distribution in the pond. The results revealed that the use of particle tracing methodology is an improved approach to define the mixing phenomenon more effectively. Moreover, the algae cell distribution aided in identifying the degree of mixing in terms of mixing length and residence time.

Numerical identification of epidemic thresholds for susceptible-infected-recovered model on finite-size networks.

Epidemic threshold has always been a very hot topic for studying epidemic dynamics on complex networks. The previous studies have provided different theoretical predictions of the epidemic threshold for the susceptible-infected-recovered (SIR) model, but the numerical verification of these theoretical predictions is still lacking. Considering that the large fluctuation of the outbreak size occurs near the epidemic threshold, we propose a novel numerical identification method of SIR epidemic threshold by analyzing the peak of the epidemic variability. Extensive experiments on synthetic and real-world networks demonstrate that the variability measure can successfully give the numerical threshold for the SIR model. The heterogeneous mean-field prediction agrees very well with the numerical threshold, except the case that the networks are disassortative, in which the quenched mean-field prediction is relatively close to the numerical threshold. Moreover, the numerical method presented is also suitable for the susceptible-infected-susceptible model. This work helps to verify the theoretical analysis of epidemic threshold and would promote further studies on the phase transition of epidemic dynamics.

Efficient allocation of heterogeneous response times in information spreading process.

Recently, the impacts of spatiotemporal heterogeneities of human activities on spreading dynamics have attracted extensive attention. In this paper, we intend to understand how the heterogeneous distribution of response times at the individual level influences information spreading. Based on the uncorrelated scale-free networks without degree-degree correlation, we study the susceptible-infected spreading dynamics with adjustable power-law response time distribution, and find that the stronger the heterogeneity of response times is, the faster the information spreading is in the early and middle stages. Following a given heterogeneity, the procedure of reducing the correlation between the response times and degrees of individuals can also accelerate the spreading dynamics in the early and middle stages. However, the dynamics in the late stage is slightly more complicated, and there is an optimal value of the full prevalence time (i.e., the time for full infection on a network) changing with the heterogeneity of response times and the response time-degree correlation, respectively. The optimal phenomena result from the efficient allocation of heterogeneous response times.

Persistent coexistence of cyclically competing species in spatially extended ecosystems.

A fundamental result in the evolutionary-game paradigm of cyclic competition in spatially extended ecological systems, as represented by the classic Reichenbach-Mobilia-Frey (RMF) model, is that high mobility tends to hamper or even exclude species coexistence. This result was obtained under the hypothesis that individuals move randomly without taking into account the suitability of their local environment. We incorporate local habitat suitability into the RMF model and investigate its effect on coexistence. In particular, we hypothesize the use of "basic instinct" of an individual to determine its movement at any time step. That is, an individual is more likely to move when the local habitat becomes hostile and is no longer favorable for survival and growth. We show that, when such local habitat suitability is taken into account, robust coexistence can emerge even in the high-mobility regime where extinction is certain in the RMF model. A surprising finding is that coexistence is accompanied by the occurrence of substantial empty space in the system. Reexamination of the RMF model confirms the necessity and the important role of empty space in coexistence. Our study implies that adaptation/movements according to local habitat suitability are a fundamental factor to promote species coexistence and, consequently, biodiversity.

Bifurcation phenomena in Taylor-Couette flow in a very short annulus with radial through-flow.

In this study, the non-linear dynamics of Taylor-Couette flow in a very small-aspect-ratio wide-gap annulus in a counter-rotating regime under the influence of radial through-flow are investigated by solving its full three-dimensional Navier-Stokes equations. Depending on the intensity of the radial flow, either an axisymmetric (pure [Formula: see text] mode) pulsating flow structure or an axisymmetric axially propagating vortex will appear subcritical, i.e. below the centrifugal instability threshold of the circular Couette flow. We show that the propagating vortices can be stably existed in two separate parameter regions, which feature different underlying dynamics. Although in one regime, the flow appears only as a limit cycle solution upon which saddle-node-invariant-circle bifurcation occurs, but in the other regime, it shows more complex dynamics with richer Hopf bifurcation sequences. That is, by presence of incommensurate frequencies, it can be appeared as 1-, 2- and 3-torus solutions, which is known as the Ruelle-Takens-Newhouse route to chaos. Therefore, the observed bifurcation scenario is the Ruelle-Takens-Newhouse route to chaos and the period doubling bifurcation, which exhibit rich and complex dynamics.

Defining the Relationship between Daily Exposure to Particulate Matter and Hospital Visits by Psoriasis Patients.

BACKGROUND: Although particulate matter likely provokes inflammatory reactions in those with chronic skin disorders like atopic dermatitis, no study has examined the relationship between particulate matter and psoriasis exacerbation. OBJECTIVE: This study evaluated possible associations between particulate matter and hospital visits for psoriasis patients in 7 major cities in South Korea. METHODS: We investigated the relationship between psoriasis and particulate matter. To do this, we used psoriasis patient data from the Korean National Health Insurance Service database. In addition, PM10 and PM2.5 concentration data spanning a 3-year time frame were obtained from the Korea Environment Corporation. RESULTS: A pattern analysis generated by the sample cross-correlation function and time series regression showed a correlation between particulate matter concentration and the number of hospital visits by psoriasis patients. However, the prewhitening method, which minimizes the effects of other variables besides particulate matter, revealed no correlation between the two. CONCLUSION: This study suggests that particulate matter has no impact on hospital visit frequency among psoriasis patients in South Korean urban areas.

Conjugate buoyant convective transport of nanofluids in an enclosed annular geometry.

A vertical annular configuration with differently heated cylindrical surfaces and horizontal adiabatic boundaries is systematically studied in view to their industrial applications. In this paper, we investigate the effects of conjugate buoyant heat transport in water based nanofluids with different nanoparticles such as alumina, titania or copper, and is filled in the enclosed annular gap. The annulus space is formed by a thick inner cylinder having a uniform high temperature, an exterior cylindrical tube with a constant lower temperature, and thermally insulated upper and lower surfaces. By investigating heat transport for broad spectrum of Rayleigh number, solid wall thickness, thermal conductivity ratio and nanoparticle volume fraction, we found that the influence of wall thickness on thermal dissipation rate along wall and interface greatly depends on conductivity ratio and vice-versa. In particular, we uncover that the choice of nanoparticle in a nanofluid and its concentration are key factors in enhancing the thermal transport along the interface. Specially, copper based nanofluids produces higher heat transport among other nanoparticles, and for the range of nanoparticle concentration chosen in this analysis, enhanced thermal dissipation along the interface has been detected as nanoparticle volume fraction is increased. Our results are applicable to choose nanofluids along with other critical parameters for the desired heat transport.

Effects of an imposed axial flow on a Ferrofluidic Taylor-Couette flow.

In this paper we investigate the effects of an externally imposed axial mass flux (axial pressure gradient, axial through flow) on ferrofluidic Taylor-Couette flow under the influence of either an axial or a transverse magnetic field. Without an imposed axial through flow, due to the symmetry-conserving axial field and the symmetry-breaking transverse field, it gives rise to various vortex flows in ferrofluidic Taylor-Couette flow such as wavy Taylor vortex flow (wTVF), wavy spiral vortex flow (wSPI) and wavy vortex flows ([Formula: see text] and [Formula: see text]), which are typically produced by a nonlinear interaction of rotational, shear and magnetic instabilities. In addition, when an axial through flow is imposed to a ferrofluidic Taylor-Couette flow in the presence of either an axial or a transverse magnetic field, previously unknown new helical vortex structures are observed. In particular, we uncover 'modulated Mixed-Cross-Spirals' with a combination of at least three different dominant azimuthal wavenumbers. Emergence of such new flow states indicates richer but potentially more controllable dynamics in ferrofluidic flows, i.e., an imposed axial through flow will be a new controllable factor/parameter in applications of a ferrofluidic and magnetic flows flow.

Multistability and arithmetically period-adding bifurcations in piecewise smooth dynamical systems.

Multistability has been a phenomenon of continuous interest in nonlinear dynamics. Most existing works so far have focused on smooth dynamical systems. Motivated by the fact that nonsmooth dynamical systems can arise commonly in realistic physical and engineering applications such as impact oscillators and switching electronic circuits, we investigate multistability in such systems. In particular, we consider a generic class of piecewise smooth dynamical systems expressed in normal form but representative of nonsmooth systems in realistic situations, and focus on the weakly dissipative regime and the Hamiltonian limit. We find that, as the Hamiltonian limit is approached, periodic attractors can be generated through a series of saddle-node bifurcations. A striking phenomenon is that the periods of the newly created attractors follow an arithmetic sequence. This has no counterpart in smooth dynamical systems. We provide physical analyses, numerical computations, and rigorous mathematical arguments to substantiate the finding.

Dynamics of ferrofluidic flow in the Taylor-Couette system with a small aspect ratio.

We investigate fundamental nonlinear dynamics of ferrofluidic Taylor-Couette flow - flow confined be-tween two concentric independently rotating cylinders - consider small aspect ratio by solving the ferro-hydrodynamical equations, carrying out systematic bifurcation analysis. Without magnetic field, we find steady flow patterns, previously observed with a simple fluid, such as those containing normal one- or two vortex cells, as well as anomalous one-cell and twin-cell flow states. However, when a symmetry-breaking transverse magnetic field is present, all flow states exhibit stimulated, finite two-fold mode. Various bifurcations between steady and unsteady states can occur, corresponding to the transitions between the two-cell and one-cell states. While unsteady, axially oscillating flow states can arise, we also detect the emergence of new unsteady flow states. In particular, we uncover two new states: one contains only the azimuthally oscillating solution in the configuration of the twin-cell flow state, and an-other a rotating flow state. Topologically, these flow states are a limit cycle and a quasiperiodic solution on a two-torus, respectively. Emergence of new flow states in addition to observed ones with classical fluid, indicates that richer but potentially more controllable dynamics in ferrofluidic flows, as such flow states depend on the external magnetic field.

Emergence of unusual coexistence states in cyclic game systems.

Evolutionary games of cyclic competitions have been extensively studied to gain insights into one of the most fundamental phenomena in nature: biodiversity that seems to be excluded by the principle of natural selection. The Rock-Paper-Scissors (RPS) game of three species and its extensions [e.g., the Rock-Paper-Scissors-Lizard-Spock (RPSLS) game] are paradigmatic models in this field. In all previous studies, the intrinsic symmetry associated with cyclic competitions imposes a limitation on the resulting coexistence states, leading to only selective types of such states. We investigate the effect of nonuniform intraspecific competitions on coexistence and find that a wider spectrum of coexistence states can emerge and persist. This surprising finding is substantiated using three classes of cyclic game models through stability analysis, Monte Carlo simulations and continuous spatiotemporal dynamical evolution from partial differential equations. Our finding indicates that intraspecific competitions or alternative symmetry-breaking mechanisms can promote biodiversity to a broader extent than previously thought.

Accurate ranking of influential spreaders in networks based on dynamically asymmetric link weights.

We propose an efficient and accurate measure for ranking spreaders and identifying the influential ones in spreading processes in networks. While the edges determine the connections among the nodes, their specific role in spreading should be considered explicitly. An edge connecting nodes i and j may differ in its importance for spreading from i to j and from j to i. The key issue is whether node j, after infected by i through the edge, would reach out to other nodes that i itself could not reach directly. It becomes necessary to invoke two unequal weights w_{ij} and w_{ji} characterizing the importance of an edge according to the neighborhoods of nodes i and j. The total asymmetric directional weights originating from a node leads to a novel measure s_{i}, which quantifies the impact of the node in spreading processes. An s-shell decomposition scheme further assigns an s-shell index or weighted coreness to the nodes. The effectiveness and accuracy of rankings based on s_{i} and the weighted coreness are demonstrated by applying them to nine real-world networks. Results show that they generally outperform rankings based on the nodes' degree and k-shell index while maintaining a low computational complexity. Our work represents a crucial step towards understanding and controlling the spread of diseases, rumors, information, trends, and innovations in networks.

Scaling laws for noise-induced super-persistent chaotic transients.

A super-persistent chaotic transient is characterized by the following scaling law for its average lifetime: tau approximately exp[C(p- p(c))(-alpha)] , where C>0 and alpha>0 are constants, p > or = p(c) is a bifurcation parameter, and p(c) is its critical value. As p approaches p(c) from above, the exponent in the exponential dependence diverges, leading to an extremely long transient lifetime. Historically the possibility of such transient raised the question of whether asymptotic attractors are relevant to turbulence. Here we investigate the phenomenon of noise-induced super-persistent chaotic transients. In particular, we construct a prototype model based on random maps to illustrate this phenomenon. We then approximate the model by stochastic differential equations and derive the scaling laws for the transient lifetime versus the noise amplitude epsilon for both the subcritical (p< p(c)) and the supercritical (p> p(c)) cases. Our results are the following. In the subcritical case where a chaotic attractor exists in the absence of noise, noise-induced transients can be more persistent in the following sense of double-exponential and algebraic scaling: tau approximately exp[K0 exp(K1epsilon(-gamma))] for small noise amplitude epsilon, where K0 >0 , K1 >0, and gamma>0 are constants. The longevity of the transient lifetime in this case is striking. For the supercritical case where there is already a super-persistent chaotic transient, noise can significantly reduce the transient lifetime. These results add to the understanding of the interplay between random and deterministic chaotic dynamics with surprising physical implications.

Magnetic field induced flow pattern reversal in a ferrofluidic Taylor-Couette system.

We investigate the dynamics of ferrofluidic wavy vortex flows in the counter-rotating Taylor-Couette system, with a focus on wavy flows with a mixture of the dominant azimuthal modes. Without external magnetic field flows are stable and pro-grade with respect to the rotation of the inner cylinder. More complex behaviors can arise when an axial or a transverse magnetic field is applied. Depending on the direction and strength of the field, multi-stable wavy states and bifurcations can occur. We uncover the phenomenon of flow pattern reversal as the strength of the magnetic field is increased through a critical value. In between the regimes of pro-grade and retrograde flow rotations, standing waves with zero angular velocities can emerge. A striking finding is that, under a transverse magnetic field, a second reversal in the flow pattern direction can occur, where the flow pattern evolves into pro-grade rotation again from a retrograde state. Flow reversal is relevant to intriguing phenomena in nature such as geomagnetic reversal. Our results suggest that, in ferrofluids, flow pattern reversal can be induced by varying a magnetic field in a controlled manner, which can be realized in laboratory experiments with potential applications in the development of modern fluid devices.

Ring-bursting behavior en route to turbulence in narrow-gap Taylor-Couette flows.

We investigate the Taylor-Couette system where the radius ratio is close to unity. Systematically increasing the Reynolds number, we observe a number of previously known transitions, such as one from the classical Taylor vortex flow (TVF) to wavy vortex flow (WVF) and the transition to fully developed turbulence. Prior to the onset of turbulence, we observe intermittent bursting patterns of localized turbulent patches, confirming the experimentally observed pattern of very short wavelength bursts (VSWBs). A striking finding is that, for a Reynolds number larger than that for the onset of VSWBs, a new type of intermittently bursting behavior emerges: patterns of azimuthally closed rings of various orders. We call them ring-bursting patterns, which surround the cylinder completely but remain localized and separated in the axial direction through nonturbulent wavy structures. We employ a number of quantitative measures including the cross-flow energy to characterize the ring-bursting patterns and to distinguish them from the background flow. These patterns are interesting because they do not occur in the wide-gap Taylor-Couette flow systems. The narrow-gap regime is less studied but certainly deserves further attention to gain deeper insights into complex flow dynamics in fluids.

Improving the accuracy of the k-shell method by removing redundant links: From a perspective of spreading dynamics.

Recent study shows that the accuracy of the k-shell method in determining node coreness in a spreading process is largely impacted due to the existence of core-like group, which has a large k-shell index but a low spreading efficiency. Based on the analysis of the structure of core-like groups in real-world networks, we discover that nodes in the core-like group are mutually densely connected with very few out-leaving links from the group. By defining a measure of diffusion importance for each edge based on the number of out-leaving links of its both ends, we are able to identify redundant links in the spreading process, which have a relatively low diffusion importance but lead to form the locally densely connected core-like group. After filtering out the redundant links and applying the k-shell method to the residual network, we obtain a renewed coreness ks for each node which is a more accurate index to indicate its location importance and spreading influence in the original network. Moreover, we find that the performance of the ranking algorithms based on the renewed coreness are also greatly enhanced. Our findings help to more accurately decompose the network core structure and identify influential nodes in spreading processes.