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Key traits of unicellular species, such as cell size, often follow scale-free or self-similar distributions, hinting at the possibility of an underlying critical process. However, linking such empirical scaling laws to the critical regime of realistic individual-based model classes is difficult. Here, we reveal new empirical scaling evidence associated with a transition in the population and the chlorophyll dynamics of phytoplankton. We offer a possible explanation for these observations by deriving scaling laws in the vicinity of the critical point of a new universality class of non-local cell growth and division models. This "criticality hypothesis" can be tested through new scaling predictions derived for our model class, for the response of chlorophyll distributions to perturbations. The derived scaling laws may also be generalized to other cellular traits and environmental drivers relevant to phytoplankton ecology.Cardiac alternans is a beat-to-beat alternation of the action potential duration (APD), which has been implicated as a possible cause of ventricular fibrillation. Previous studies have shown that alternans can originate via a period doubling bifurcation caused by the nonlinear dependence of the APD on the previous diastolic interval. In this case, it has been demonstrated that alternans can be eliminated by applying feedback control on the pacing cycle length. However, studies have shown that alternans can also originate due to unstable calcium (Ca) cycling in cardiac myocytes. In this study, we explore the effectiveness of APD feedback control to suppress alternans when the underlying instability is due to unstable Ca cycling. In particular, we explore the role of the bi-directional coupling between Ca and voltage and determine the effectiveness of feedback control under a wide range of conditions. We also analyze the applicability of feedback control on a coupled two cell system and show that APD control induces spatially out-of-phase alternans. We analyze the onset and the necessary conditions for the emergence of these out-of-phase patterns and assess the effectiveness of feedback control to suppress Ca driven alternans in a multi-cellular system.Despite the importance of having robust estimates of the time-asymptotic total number of infections, early estimates of COVID-19 show enormous fluctuations. Using COVID-19 data from different countries, we show that predictions are extremely sensitive to the reporting protocol and crucially depend on the last available data point before the maximum number of daily infections is reached. We propose a physical explanation for this sensitivity, using a susceptible-exposed-infected-recovered model, where the parameters are stochastically perturbed to simulate the difficulty in detecting patients, different confinement measures taken by different countries, as well as changes in the virus characteristics. Our results suggest that there are physical and statistical reasons to assign low confidence to statistical and dynamical fits, despite their apparently good statistical scores. These considerations are general and can be applied to other epidemics.Cyber-physical systems (CPSs) are integrations of information technology and physical systems, which are more and more significant in society. As a typical example of CPSs, smart grids integrate many advanced devices and information technologies to form a safer and more efficient power system. However, interconnection with the cyber network makes the system more complex, so that the robustness assessment of CPSs becomes more difficult. This paper proposes a new CPS model from a complex network perspective. We try to consider the real dynamics of cyber and physical parts and the asymmetric interdependency between them. [https://www.selleckchem.com/products/tng260.html selleck chemicals llc] Simulation results show that coupling with the communication network makes better robustness of power system. But since the influences between the power and communication networks are asymmetric, the system parameters play an important role to determine the robustness of the whole system.Influential nodes identification problem (INIP) is one of the most important problems in complex networks. Existing methods mainly deal with this problem in undirected networks, while few studies focus on it in directed networks. Moreover, the methods designed for identifying influential nodes in undirected networks do not work for directed networks. Therefore, in this paper, we investigate INIP in directed networks. We first propose a novel metric to assess the influence effect of nodes in directed networks. Then, we formulate a compact model for INIP and prove it to be NP-Complete. Furthermore, we design a novel heuristic algorithm for the proposed model by integrating a 2-opt local search into a greedy framework. The experimental results show that, in most cases, the proposed methods outperform traditional measure-based heuristic methods in terms of accuracy and discrimination.The well-known cubic Allen-Cahn (AC) equation is a simple gradient dynamics (or variational) model for a nonconserved order parameter field. After revising main literature results for the occurrence of different types of moving fronts, we employ path continuation to determine their bifurcation diagram in dependence of the external field strength or chemical potential. We then employ the same methodology to systematically analyze fronts for more involved AC-type models. In particular, we consider a cubic-quintic variational AC model and two different nonvariational generalizations. We determine and compare the bifurcation diagrams of front solutions in the four considered models.In this paper, the Ricker family (a population model) with quasiperiodic excitation is considered. The existence of strange nonchaotic attractors (SNAs) is analyzed in a co-dimension-2 parameter space by both theoretical and numerical methods. We prove that SNAs exist in a positive measure parameter set. The SNAs are nowhere differentiable (i.e., strange). We use numerical methods to identify the existence of SNAs in a larger parameter set. The nonchaotic property of SNAs is verified by evaluating the Lyapunov exponents, while the strange property is characterized by phase sensitivity and rational approximations. We also find that there is a transition region in a parameter plane in which SNAs alternate with chaotic attractors.Complex dynamical systems can shift abruptly from a stable state to an alternative stable state at a tipping point. Before the critical transition, the system either slows down in its recovery rate or flickers between the basins of attraction of the alternative stable states. Whether the heart critically slows down or flickers before it transitions into and out of paroxysmal atrial fibrillation (PAF) is still an open question. To address this issue, we propose a novel definition of cardiac states based on beat-to-beat (RR) interval fluctuations derived from electrocardiogram data. Our results show the cardiac state flickers before PAF onset and termination. Prior to onset, flickering is due to a "tug-of-war" between the sinus node (the natural pacemaker) and atrial ectopic focus/foci (abnormal pacemakers), or the pacing by the latter interspersed among the pacing by the former. It may also be due to an abnormal autonomic modulation of the sinus node. This abnormal modulation may be the sole cause of flickering prior to termination since atrial ectopic beats are absent. Flickering of the cardiac state could potentially be used as part of an early warning or screening system for PAF and guide the development of new methods to prevent or terminate PAF. The method we have developed to define system states and use them to detect flickering can be adapted to study critical transition in other complex systems.By means of Galerkin-Koornwinder (GK) approximations, an efficient reduction approach to the Stuart-Landau (SL) normal form and center manifold is presented for a broad class of nonlinear systems of delay differential equations that covers the cases of discrete as well as distributed delays. The focus is on the Hopf bifurcation as a consequence of the critical equilibrium's destabilization resulting from an eigenpair crossing the imaginary axis. The nature of the resulting Hopf bifurcation (super- or subcritical) is then characterized by the inspection of a Lyapunov coefficient easy to determine based on the model's coefficients and delay parameters. We believe that our approach, which does not rely too much on functional analysis considerations but more on analytic calculations, is suitable to concrete situations arising in physics applications. Thus, using this GK approach to the Lyapunov coefficient and the SL normal form, the occurrence of Hopf bifurcations in the cloud-rain delay models of Koren and Feingold (KF) on one hand and Koren, Tziperman, and Feingold on the other are analyzed. Noteworthy is the existence of the KF model of large regions of the parameter space for which subcritical and supercritical Hopf bifurcations coexist. These regions are determined, in particular, by the intensity of the KF model's nonlinear effects. "Islands" of supercritical Hopf bifurcations are shown to exist within a subcritical Hopf bifurcation "sea"; these islands being bordered by double-Hopf bifurcations occurring when the linearized dynamics at the critical equilibrium exhibit two pairs of purely imaginary eigenvalues.This paper proposes a simple no-equilibrium chaotic system with only one signum function as compared with the existing no-equilibrium chaotic ones with at least one quadratic or higher nonlinearity. The system has the offset boosting of three variables through adjusting the corresponding controlled constants. The resulting hidden attractors can be distributed in a 1D line, a 2D lattice, a 3D grid, and even in an arbitrary location of the phase space. Particularly, a hidden chaotic bursting oscillation is also observed in this system, which is an uncommon phenomenon. In addition, complex hidden dynamics is investigated via phase portraits, time series, Kaplan-Yorke dimensions, bifurcation diagrams, Lyapunov exponents, and two-parameter bifurcation diagrams. Then, a very simple hardware circuit without any multiplier is fabricated, and the experimental results are presented to demonstrate theoretical analyses and numerical simulations. Furthermore, the randomness test of the chaotic pseudo-random sequence generated by the system is tested by the National Institute of Standards and Technology test suite. The tested results show that the proposed system has good randomness, thus being suitable for chaos-based applications such as secure communication and image encryption.We study a heterogeneous population consisting of two groups of oscillatory elements, one with attractive and one with repulsive coupling. Moreover, we set different internal timescales for the oscillators of the two groups and concentrate on the role of this timescale separation in the collective behavior. Our results demonstrate that it may significantly modify synchronization properties of the system, and the implications are fundamentally different depending on the ratio between the group timescales. For the slower attractive group, synchronization properties are similar to the case of equal timescales. However, when the attractive group is faster, these properties significantly change and bistability appears. The other collective regimes such as frozen states and solitary states are also shown to be crucially influenced by timescale separation.