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Possible distribution of the very most confronted kinds Ostrya rehderiana (Betulaceae) within Cina underneath long term climate change.
The theory of motion of edges of dispersive shock waves generated after wave breaking of simple waves is developed. It is shown that this motion obeys Hamiltonian mechanics complemented by a Hopf-like equation for evolution of the background flow, which interacts with the edge wave packets or the edge solitons. A conjecture about the existence of a certain symmetry between equations for the small-amplitude and soliton edges is formulated. In the case of localized simple-wave pulses propagating through a quiescent medium, this theory provided a new approach to derivation of an asymptotic formula for the number of solitons eventually produced from such a pulse.The simplest ring oscillator is made from three strongly nonlinear elements repressing each other unidirectionally, resulting in the emergence of a limit cycle. A popular implementation of this scheme uses repressor genes in bacteria, creating the synthetic genetic oscillator known as the Repressilator. We consider the main collective modes produced when two identical Repressilators are mean-field-coupled via the quorum-sensing mechanism. In-phase and anti-phase oscillations of the coupled oscillators emerge from two Andronov-Hopf bifurcations of the homogeneous steady state. Using the rate of the repressor's production and the value of coupling strength as the bifurcation parameters, we performed one-parameter continuations of limit cycles and two-parameter continuations of their bifurcations to show how bifurcations of the in-phase and anti-phase oscillations influence the dynamical behaviors for this system. Pitchfork bifurcation of the unstable in-phase cycle leads to the creation of novel inhomogeneous limit cycles with very different amplitudes, in contrast to the well-known asymmetrical limit cycles arising from oscillation death. The Neimark-Sacker bifurcation of the anti-phase cycle determines the border of an island in two-parameter space containing almost all the interesting regimes including the set of resonant limit cycles, the area with stable inhomogeneous cycle, and very large areas with chaotic regimes resulting from torus destruction and period doubling of resonant cycles and inhomogeneous cycles. We discuss the structure of the chaos skeleton to show the role of inhomogeneous cycles in its formation. Many regions of multistability and transitions between regimes are presented. These results provide new insights into the coupling-dependent mechanisms of multistability and collective regime symmetry breaking in populations of identical multidimensional oscillators.In this article, we construct a kind of three-dimensional piecewise linear (PWL) system with three switching manifolds and obtain four theorems with regard to the existence of a homoclinic orbit and a heteroclinic cycle in this class of PWL system. The first theorem studies the existence of a heteroclinic cycle connecting two saddle-foci. The existence of a homoclinic orbit connecting one saddle-focus is investigated in the second theorem, and the third theorem examines the existence of a homoclinic orbit connecting another saddle-focus. The last one proves the coexistence of the heteroclinic cycle and two homoclinic orbits for the same parameters. Numerical simulations are given as examples and the results are consistent with the predictions of theorems.We study patterns of partial synchronization in a network of FitzHugh-Nagumo oscillators with empirical structural connectivity measured in human subjects. We report the spontaneous occurrence of synchronization phenomena that closely resemble the ones seen during epileptic seizures in humans. In order to obtain deeper insights into the interplay between dynamics and network topology, we perform long-term simulations of oscillatory dynamics on different paradigmatic network structures random networks, regular nonlocally coupled ring networks, ring networks with fractal connectivities, and small-world networks with various rewiring probability. Among these networks, a small-world network with intermediate rewiring probability best mimics the findings achieved with the simulations using the empirical structural connectivity. For the other network topologies, either no spontaneously occurring epileptic-seizure-related synchronization phenomena can be observed in the simulated dynamics, or the overall degree of synchronization remains high throughout the simulation. This indicates that a topology with some balance between regularity and randomness favors the self-initiation and self-termination of episodes of seizure-like strong synchronization.A multilayer approach has recently received particular attention in network neuroscience as a suitable model to describe brain dynamics by adjusting its activity in different frequency bands, time scales, modalities, or ages to different layers of a multiplex graph. click here In this paper, we demonstrate an approach to a frequency-based multilayer functional network constructed from nonstationary multivariate data by analyzing recurrences in application to electroencephalography. Using the recurrence-based index of synchronization, we construct intralayer (within-frequency) and interlayer (cross-frequency) graph edges to model the evolution of a whole-head functional connectivity network during a prolonged stimuli classification task. We demonstrate that the graph edges' weights increase during the experiment and negatively correlate with the response time. We also show that while high-frequency activity evolves toward synchronization of remote local areas, low-frequency connectivity tends to establish large-scale coupling between them.The generation of walking patterns is central to bio-inspired robotics and has been attained using methods encompassing diverse numerical as well as analog implementations. Here, we demonstrate the possibility of synthesizing viable gaits using a paradigmatic low-dimensional non-linear entity, namely, the Rössler system, as a dynamical unit. Through a minimalistic network wherein each instance is univocally associated with one leg, it is possible to readily reproduce the canonical gaits as well as generate new ones via changing the coupling scheme and the associated delays. Varying levels of irregularity can be introduced by rendering individual systems or the entire network chaotic. Moreover, through tailored mapping of the state variables to physical angles, adequate leg trajectories can be accessed directly from the coupled systems. The functionality of the resulting generator was confirmed in laboratory experiments by means of an instrumented six-legged ant-like robot. Owing to their simple form, the 18 coupled equations could be rapidly integrated on a bare-metal microcontroller, leading to the demonstration of real-time robot control navigating an arena using a brain-machine interface.Reservoir computing has repeatedly been shown to be extremely successful in the prediction of nonlinear time-series. However, there is no complete understanding of the proper design of a reservoir yet. We find that the simplest popular setup has a harmful symmetry, which leads to the prediction of what we call mirror-attractor. We prove this analytically. Similar problems can arise in a general context, and we use them to explain the success or failure of some designs. The symmetry is a direct consequence of the hyperbolic tangent activation function. Furthermore, four ways to break the symmetry are compared numerically A bias in the output, a shift in the input, a quadratic term in the readout, and a mixture of even and odd activation functions. First, we test their susceptibility to the mirror-attractor. Second, we evaluate their performance on the task of predicting Lorenz data with the mean shifted to zero. The short-time prediction is measured with the forecast horizon while the largest Lyapunov exponent and the correlation dimension are used to represent the climate. Finally, the same analysis is repeated on a combined dataset of the Lorenz attractor and the Halvorsen attractor, which we designed to reveal potential problems with symmetry. link2 We find that all methods except the output bias are able to fully break the symmetry with input shift and quadratic readout performing the best overall.The active Phase-Field-Crystal (aPFC) model combines elements of the Toner-Tu theory for self-propelled particles and the classical Phase-Field-Crystal (PFC) model that describes the transition between liquid and crystalline phases. In the liquid-crystal coexistence region of the PFC model, crystalline clusters exist in the form of localized states that coexist with a homogeneous background. At sufficiently strong activity (related to self-propulsion strength), they start to travel. We employ numerical path continuation and direct time simulations to first investigate the existence regions of different types of localized states in one spatial dimension. The results are summarized in morphological phase diagrams in the parameter plane spanned by activity and mean density. Then we focus on the interaction of traveling localized states, studying their collision behavior. As a result, we distinguish "elastic" and "inelastic" collisions. In the former, localized states recover their properties after a collision, while in the latter, they may completely or partially annihilate, forming resting bound states or various traveling states.City taxi service systems have been empirically studied by a number of data-driven methods. However, their underlying mechanisms are hard to understand because the present mathematical models neglect to explain a (whole) taxi service process that includes a pair of on-load phase and off-load phase. In this paper, by analyzing a large amount of taxi servicing data from a large city in China, we observe that the taxi service process shows different temporal and spatial features according to the on-load phase and off-load phase. Moreover, our correlation analysis results demonstrate the lack of dependence between the on-load phase and the off-load phase. Hence, we introduce two independent random walk models based on the Langevin equation to describe the underlying mechanism and to understand the temporal and spatial features of the taxi service process. Our study attempts to formulate the mathematical framework for simulating the taxi service process and better understanding of its underlying mechanism.We extend the recently developed generalized Floquet theory [Phys. Rev. Lett. 110, 170602 (2013)] to systems with infinite memory, i.e., a dependence on the whole previous history. In particular, we show that a lower asymptotic bound exists for the Floquet exponents associated to such cases. As examples, we analyze the cases of an ideal 1D system, a Brownian particle, and a circuit resonator with an ideal transmission line. All these examples show the usefulness of this new approach to the study of dynamical systems with memory, which are ubiquitous in science and technology.In this paper, we present an explicit Darboux transformation of the generalized mixed nonlinear Schrödinger (GMNLS) equation. The compact determinant representation of the n-fold Darboux transformation of the GMNLS equation is constructed and the nth-order solution is built. link3 We further prove that only the even-fold Darboux transformation and the even-order solution of the GMNLS equation can, respectively, be reduced to the Darboux transformation and solution of the Kundu-Eckhaus equation. Furthermore, two different kinds of explicit one-soliton solutions of the GMNLS equation are constructed and discussed.
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