Dynamical Analysis and Periodic Solution of a Chaotic System with Coexisting Attractors

Chaotic attractors with no equilibria, with an unstable node, and with stable node-focus are presented in this paper. The conservative solutions are investigated by the semianalytical and seminumerical method. Furthermore, multiple coexisting attractors are investigated, and circuit is carried out. To study the system’s global structure, dynamics at infinity for this new chaotic system are studied using Poincaré compactification of polynomial vector fields in R 3 . Meanwhile, the dynamics near the infinity of the singularities are obtained by reducing the system’s dimensions on a Poincaré ball. The averaging theory analyzes the periodic solution’s stability or instability that bifurcates from Hopf-zero bifurcation.

Bipolar Pulse-Induced Coexisting Firing Patterns in Two-Dimensional Hindmarsh–Rose Neuron Model

In this paper, a bipolar pulse (BP) current is taken to mimic a periodic stimulus effect on the membrane potential in the axon of a neuron. By introducing the BP current to substitute the externally applied constant current, a BP-forced two-dimensional Hindmarsh–Rose (HR) neuron model is proposed. Based on the proposed neuron model, the BP-switched equilibrium point and its stability evolution with the periodic variation in time are explored. Furthermore, coexisting asymmetric attractors (or coexisting firing patterns) with bistability are revealed by phase plane orbits, time sequences, and attraction basins, as well as the BP-induced coexisting asymmetric attractors’ behaviors are then elaborated through bifurcation analysis. The research results exhibit that, with the increase of the time, the stabilities of the neuron model are continually switched between an unstable node-focus and a stable point, resulting in the coexisting behaviors of numerous asymmetric attractors under the specified initials. Consequently, the newly introduced BP current stimulus, instead of the original constant current stimulus, allows the two-dimensional HR neuron model to possess complex dynamical behaviors for the membrane potential. Additionally, a hardware breadboard is fabricated and circuit experiments are carried out to validate the numerical simulations.

The anatomy of an unstable node: a Levantine relict precipitates phylogenomic dissolution of higher-level relationships of the armoured harvestmen (Arachnida: Opiliones: Laniatores)

After tumultuous revisions to the family-level systematics of Laniatores (the armored harvestmen), the basally branching family Phalangodidae presently bears a disjunct and irregular distribution, attributed to the fragmentation of Pangea. One of the curious lineages assigned to Phalangodidae is the monotypic Israeli genus Haasus, the only Laniatores species that occurs in Israel, and whose presence in the Levant has been inferred to result from biogeographic connectivity with Eurasia. Recent surveys of Israeli caves have also yielded a new troglobitic morphospecies of Haasus. Here, we describe this new species as Haasus naasane sp. nov. So as to test the biogeographic affinity of Haasus, we sequenced DNA from both species and RNA from Haasus naasane sp. nov., to assess their phylogenetic placement. Our results showed that the new species is clearly closely related to Haasus judaeus, but Haasus itself is unambiguously nested within the largely Afrotropical family Pyramidopidae. In addition, the Japanese ‘phalangodid’ Proscotolemon sauteri was recovered as nested within the Southeast Asian family Petrobunidae. Phylogenomic placement of Haasus naasane sp. nov. in a 1550-locus matrix indicates that Pyramidopidae has an unstable position in the tree of Laniatores, with alternative partitioning of the matrix recovering high nodal support for mutually exclusive tree topologies. Exploration of phylogenetic signal showed the cause of this instability to be a considerable conflict between partitions, suggesting that the basal phylogeny of Laniatores may not yet be stable to addition of taxa. We transfer Haasus to Pyramidopidae (new familial assignment). Additionally, we transfer Proscotolemon to the family Petrobunidae (new familial assignment). Future studies on basal Laniatores phylogeny should emphasise the investigation of small-bodied and obscure groups that superficially resemble Phalangodidae.

Flow topology in compressible turbulent boundary layer

The flow topologies of compressible turbulent boundary layers at Mach 2 are investigated by means of direct numerical simulation (DNS) of the compressible Navier–Stokes equations, and statistical analysis of the invariants of the velocity gradient tensor. We identify a preference for an unstable focus/compressing topology in the inner layer and an unstable node/saddle/saddle (UN/S/S) topology in the outer layer. The dissipation and dissipation production originate mainly from this UN/S/S topology. The enstrophy depends mainly on an unstable focus/stretching (UFS) topology, and the enstrophy production relies on a UN/S/S topology in the inner layer and on a UFS topology in the outer layer. The compressibility effect on the statistical properties of the topologies is investigated in terms of the ‘incompressible’, compressed and expanding regions. It is found that the locally compressed region tends to be more stable and the locally expanding region tends to be more dissipative. The compressibility is mainly related to unstable focus/compressing and stable focus/stretching topologies. Moreover, the features of the average dissipation, enstrophy, dissipation production and enstrophy production of the various topologies are clarified in the locally compressed and expanding regions.

Study on the Volatility Order of Systems with Two Minimum Azeotropes

In systems with two minimum binary azeotropes, there are two isovolatility lines. Different volatility order can be obtained according to different isovolatility lines. The volatility orders of components are identified according to the isovolatility lines and are compared with that identified based on the rigorous simulation using Aspen Plus. The results show that, in the system with two minimum binary azeotropes and two isovolatility lines, the volatility order of components is determined by the isovolatility line passing through the unstable node. Based on this, the rule for identifying the volatility order is proposed. The case studies show that this rule is simple and feasible.This template explains and demonstrates how to prepare your camera-ready paper for Trans Tech Publications. The best is to read these instructions and follow the outline of this text.