Chaos: An Interdisciplinary Journal of Nonlinear Science is a peerreviewed journal devoted to increasing the understanding of nonlinear phenomena. Chaos is committed to publish selective and high quality content that is accessible to researchers from a broad spectrum of disciplines. Topics cover nonlinear dynamical systems, neural networks and neurodynamics, climate and earth sciences, condensed matter, fluid dynamics, synchronization, turbulence, solitons and coherent structures, timeseries analysis, and more.
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Cells in the brain's Suprachiasmatic Nucleus (SCN) are known to regulate circadian rhythms in mammals. We model synchronization of SCN cells using the forced Kuramoto model, which consists of a large population of coupled phase oscillators (modeling individual SCN cells) with heterogeneous intrinsic frequencies and external periodic forcing. Here, the periodic forcing models diurnally varying external inputs such as sunrise, sunset, and alarm clocks. We reduce the dimensionality of the system using the ansatz of Ott and Antonsen and then study the effect of a sudden change of clock phase to simulate crosstimezone travel. We estimate model parameters from previous biological experiments. By examining the phase space dynamics of the model, we study the mechanism leading to the difference typically experienced in the severity of jetlag resulting from eastward and westward travel.

We study the dynamics of coupled phase oscillators on a twodimensional Kuramoto lattice with periodic boundary conditions. For coupling strengths just below the transition to global phaselocking, we find localized spatiotemporal patterns that we call “frequency spirals.” These patterns cannot be seen under time averaging; they become visible only when we examine the spatial variation of the oscillators' instantaneous frequencies, where they manifest themselves as twoarmed rotating spirals. In the more familiar phase representation, they appear as wobbly periodic patterns surrounding a phase vortex. Unlike the stationary phase vortices seen in magnetic spin systems, or the rotating spiral waves seen in reactiondiffusion systems, frequency spirals librate: the phases of the oscillators surrounding the central vortex move forward and then backward, executing a periodic motion with zero winding number. We construct the simplest frequency spiral and characterize its properties using analytical and numerical methods. Simulations show that frequency spirals in large lattices behave much like this simple prototype.

This paper generalizes the stability test method via integral estimation for integerorder neutral timedelay systems to neutral fractionaldelay systems. The key step in stability test is the calculation of the number of unstable characteristic roots that is described by a definite integral over an interval from zero to a sufficient large upper limit. Algorithms for correctly estimating the upper limits of the integral are given in two concise ways, parameter dependent or independent. A special feature of the proposed method is that it judges the stability of fractionaldelay systems simply by using rough integral estimation. Meanwhile, the paper shows that for some neutral fractionaldelay systems, the stability is extremely sensitive to the change of time delays. Examples are given for demonstrating the proposed method as well as the delay sensitivity.

This paper proposes a novel approach for generating multiscroll chaotic attractors in multidirections for fractionalorder (FO) systems. The stair nonlinear function series and the saturated nonlinear function are combined to extend equilibrium points with index 2 in a new FO linear system. With the help of stability theory of FO systems, stability of its equilibrium points is analyzed, and the chaotic behaviors are validated through phase portraits, Lyapunov exponents, and Poincaré section. Choosing the order 0.96 as an example, a circuit for generating 2D grid multiscroll chaotic attractors is designed, and 2D 9 × 9 grid FO attractors are observed at most. Numerical simulations and circuit experimental results show that the method is feasible and the designed circuit is correct.

Mathematical models provide a mathematical description of neuron activity, which can better understand and quantify neural computations and corresponding biophysical mechanisms evoked by stimulus. In this paper, based on the output spike train evoked by the acupuncture mechanical stimulus, we present two different levels of models to describe the inputoutput system to achieve the reconstruction of neuronal input. The reconstruction process is divided into two steps: First, considering the neuronal spiking event as a Gamma stochastic process. The scale parameter and the shape parameter of Gamma process are, respectively, defined as two spiking characteristics, which are estimated by a statespace method. Then, leaky integrateandfire (LIF) model is used to mimic the response system and the estimated spiking characteristics are transformed into two temporal input parameters of LIF model, through two conversion formulas. We test this reconstruction method by three different groups of simulation data. All three groups of estimates reconstruct input parameters with fairly high accuracy. We then use this reconstruction method to estimate the nonmeasurable acupuncture input parameters. Results show that under three different frequencies of acupuncture stimulus conditions, estimated input parameters have an obvious difference. The higher the frequency of the acupuncture stimulus is, the higher the accuracy of reconstruction is.