Singular Orbits and Dynamics at Infinity of a Conjugate Lorenz-Like System

A conjugate Lorenz-like system which includes only two quadratic nonlinearities is proposed in this paper. Some basic properties of this system, such as the distribution of its equilibria and their stabilities, the Lyapunov exponents, the bifurcations are investigated by some numerical and theoretical analysis. The forming mechanisms of compound structures of its new chaotic attractors obtained by merging together two simple attractors after performing one mirror operation are also presented. Furthermore, some of its other complex dynamical behaviours, which include the existence of singularly degenerate heteroclinic cycles, the existence of homoclinic and heteroclinic orbits and the dynamics at infinity, etc, are formulated in detail. In the meantime, some problems deserving further investigations are presented

Bifurcation of Nongeneric Homoclinic Orbit Accompanied by Pitchfork Bifurcation

The bifurcation of a nongeneric homoclinic orbit (i.e., the orbit comes from the equilibrium along the unstable manifold instead of the center manifold) connecting a nonhyperbolic equilibrium is investigated, and the nonhyperbolic equilibrium undergoes a pitchfork bifurcation. The existence (resp., nonexistence) of a homoclinic orbit and an 1-periodic orbit are established when the pitchfork bifurcation does not happen, while as the nonhyperbolic equilibrium undergoes a pitchfork bifurcation, we obtain the sufficient conditions for the existence of homoclinic orbit and two or three heteroclinic orbits, and so forth. Moreover, we explore the difference between the bifurcation of the nongeneric homoclinic orbit and the generic one

Dynamical Analysis and Simulation of a New Lorenz-Like Chaotic System

This work presents and investigates a new chaotic system with eight terms. By numerical simulation, the two-scroll chaotic attractor is found for some certain parameters. And, by theoretical analysis, we discuss the dynamical behavior of the new-type Lorenz-like chaotic system. Firstly, the local dynamical properties, such as the distribution and the local stability of all equilibrium points, the local stable and unstable manifolds, and the Hopf bifurcations, are all revealed as the parameters varying in the space of parameters. Secondly, by applying the way of Poincaré compactification in ℝ3, the dynamics at infinity are clearly analyzed. Thirdly, combining the dynamics at finity and those at infinity, the global dynamical behaviors are formulated. Especially, we have proved the existence of the infinite heteroclinic orbits. Furthermore, all obtained theoretical results in this paper are further verified by numerical simulations

The Twisting Bifurcations of Double Homoclinic Loops with Resonant Eigenvalues

The twisting bifurcations of double homoclinic loops with resonant eigenvalues are investigated in four-dimensional systems. The coexistence or noncoexistence of large 1-homoclinic orbit and large 1-periodic orbit near double homoclinic loops is given. The existence or nonexistence of saddle-node bifurcation surfaces is obtained. Finally, the complete bifurcation diagrams and bifurcation curves are also given under different cases. Moreover, the methods adopted in this paper can be extended to a higher dimensional system

Endovascular therapy in acute ischaemic stroke with large infarction with matched or mismatched clinical-radiological severities: a post-hoc analysis of the ANGEL-ASPECT trialResearch in context

Summary: Background: Endovascular therapy (EVT) was demonstrated effective in acute large vessel occlusion (LVO) with large infarction. Revealing subgroups of patients who would or would not benefit from EVT will further inform patient selection for EVT. Methods: This post-hoc analysis of the ANGEL-ASPECT trial, a randomised controlled trial of 456 adult patients with acute anterior-circulation LVO and large infarction, defined by ASPECTS 3–5 or infarct core volume 70–100 mL, enrolled from 46 centres across China, between October 2, 2020 and May 18, 2022. Patients were randomly assigned (1:1) to receiving EVT and medical management or medical management alone. One patient withdrew consent, 455 patients were included in this post-hoc analysis and categorised into 4 subgroups by lower or higher NIHSS (< or ≥16) and smaller or larger infarct core (< or ≥70 mL). Those with lower NIHSS &amp; smaller core, and higher NIHSS &amp; larger core were considered clinical-radiological matched subgroups; otherwise clinical-radiological mismatched subgroups. Primary outcome was 90-day modified Rankin Scale (mRS). ANGEL-ASPECT is registered with ClinicalTrials.gov, NCT04551664. Findings: Overall, 139 (30.5%) patients had lower NIHSS &amp; smaller core, 106 (23.3%) higher NIHSS &amp; larger core, 130 (28.6%) higher NIHSS &amp; smaller core, and 80 (17.6%) lower NIHSS &amp; larger core. There was significant ordinal shift in the 90-day mRS toward a better outcome with EVT in clinical-radiological matched subgroups: lower NIHSS &amp; smaller core (generalised OR, 1.76; 95% CI, 1.18–2.62; p = 0.01) and higher NIHSS &amp; larger core (1.64; 1.06–2.54; 0.01); but not in the two clinical-radiological mismatched subgroups. Interpretation: Our findings suggested that in patients with anterior-circulation LVO and large infarction, EVT was associated with improved 90-day functional outcomes in those with matched clinical and radiological severities, but not in those with mismatched clinical and radiological severities. Simultaneous consideration of stroke severity and infarct core volume may inform patient selection for EVT. Funding: Unrestricted grants from industry [Covidien Healthcare International Trading (Shanghai), Johnson &amp; Johnson MedTech, Genesis MedTech (Shanghai), and Shanghai HeartCare Medical Technology]