arXiv subjects

Junfeng Cheng

Publications and source records attributed to Junfeng Cheng.

5 recordsLinked to original sources

arXiv2026

Topological Horseshoe Induced by Periodic Switching Between Non-Isochronous Planar Systems

We establish a criterion for the existence of a topological horseshoe in a class of planar systems generated by periodic switching between two subsystems, each admitting a family of closed orbits, where the mechanism for chaos arises from the non-isochronicity of each subsystem. Exploiting the relationship between the period function of a Hamiltonian system and the rate of change of the area enclosed by its periodic orbits, we derive a criterion, which can be checked by numerical methods, for the existence of horseshoe in planar systems obtained by switching between two Hamiltonian subsystems. Furthermore, by invoking monotonicity results for the period function in Newtonian Hamiltonian systems, we obtain an explicit and computable criterion that guarantees chaotic dynamics in planar systems generated by switching between two such subsystems.

math.DS↗

arXiv2025

Variation of entropy in the Duffing system with the amplitude of the external force

In this paper, we revisit the well-known perturbed Duffing system and investigate its chaotic dynamics by means of numerical Runge--Kutta method based on topological horseshoe theory. Precisely, we investigate chaos through the topological horseshoes associated with the first, second, and third return maps, obtained by varying the amplitude of an external force term while keeping all other parameters fixed. Our new finding demonstrates that, when the force amplitude exceeds a certain value, the topological (Smale) horseshoe degenerates into a pseudo-horseshoe, while chaotic invariant set persists. This phenomenon indicates that the lower bound of the topological entropy decreases as the force amplitude increases, thereby enriching the dynamics in the perturbed Duffing system. Furthermore, we identify a critical value of the force amplitude governing the attractivity of the chaotic invariant set. For amplitudes slightly below this value, the basin of attraction of the chaotic invariant set progressively shrinks as the amplitude increases. In contrast, for larger amplitudes, both Lyapunov exponents become negative while the topological horseshoe persists, suggesting that the chaotic invariant set loses attractivity as the amplitude grows.

nlin.CD↗

arXiv2025

Incomplete crossing and semi-topological horseshoes

This paper enriches the topological horseshoe theory using finite subshift theory in symbolic dynamical systems, and develops an elementary framework addressing incomplete crossing and semi-horseshoes. Two illustrative examples are provided: one from the perturbed Duffing system and another from a polynomial system proposed by Chen, demonstrating the prevalence of semi-horseshoes in chaotic systems. Moreover, the semi-topological horseshoe theory enhances the detection of chaos and improves the accuracy of topological entropy estimation.

math.DS↗

arXiv2024

G-FARS: Gradient-Field-based Auto-Regressive Sampling for 3D Part Grouping

This paper proposes a novel task named "3D part grouping". Suppose there is a mixed set containing scattered parts from various shapes. This task requires algorithms to find out every possible combination among all the parts. To address this challenge, we propose the so called Gradient Field-based Auto-Regressive Sampling framework (G-FARS) tailored specifically for the 3D part grouping task. In our framework, we design a gradient-field-based selection graph neural network (GNN) to learn the gradients of a log conditional probability density in terms of part selection, where the condition is the given mixed part set. This innovative approach, implemented through the gradient-field-based selection GNN, effectively captures complex relationships among all the parts in the input. Upon completion of the training process, our framework becomes capable of autonomously grouping 3D parts by iteratively selecting them from the mixed part set, leveraging the knowledge acquired by the trained gradient-field-based selection GNN. Our code is available at: https://github.com/J-F-Cheng/G-FARS-3DPartGrouping.

cs.CV↗

arXiv2023

Score-PA: Score-based 3D Part Assembly

Autonomous 3D part assembly is a challenging task in the areas of robotics and 3D computer vision. This task aims to assemble individual components into a complete shape without relying on predefined instructions. In this paper, we formulate this task from a novel generative perspective, introducing the Score-based 3D Part Assembly framework (Score-PA) for 3D part assembly. Knowing that score-based methods are typically time-consuming during the inference stage. To address this issue, we introduce a novel algorithm called the Fast Predictor-Corrector Sampler (FPC) that accelerates the sampling process within the framework. We employ various metrics to assess assembly quality and diversity, and our evaluation results demonstrate that our algorithm outperforms existing state-of-the-art approaches. We release our code at https://github.com/J-F-Cheng/Score-PA_Score-based-3D-Part-Assembly.

cs.CV↗