For general nonautonomous systems, integral sets similar to homoclinic structures of an autonomous system are introduced. A description of integral curves near such a set is given.

Download full-text PDF

Source
http://dx.doi.org/10.1063/1.165887DOI Listing

Publication Analysis

Top Keywords

nonautonomous systems
8
homoclinical structures
4
structures nonautonomous
4
systems nonautonomous
4
nonautonomous chaos
4
chaos general
4
general nonautonomous
4
systems integral
4
integral sets
4
sets homoclinic
4

Similar Publications

Compartmental Models Driven by Renewal Processes: Survival Analysis and Applications to SVIS Epidemic Models.

Sci Rep

January 2025

Department of Biostatistics, Data Science and Epidemiology, School of Public Health, Augusta University, 1120, 15th Street, Augusta, GA, 30912, USA.

Compartmental models with exponentially distributed lifetime stages assume a constant hazard rate, limiting their scope. This study develops a theoretical framework for systems with general lifetime distributions, modeled as transition rates in a renewal process. Applications are provided for the SVIS (Susceptible-Vaccinated-Infected-Susceptible) disease epidemic model to investigate the impacts of hazard rate functions (HRFs) on disease control.

View Article and Find Full Text PDF

Many existing control techniques proposed in the literature tend to overlook faults and physical limitations in the systems, which significantly restricts their applicability to practical, real-world systems. Consequently, there is an urgent necessity to advance the control and synchronization of such systems in real-world scenarios, specifically when faced with the challenges posed by faults and physical limitations in their control actuators. Motivated by this, our study unveils an innovative control approach that combines a neural network-based sliding mode algorithm with fuzzy logic systems to handle nonlinear systems.

View Article and Find Full Text PDF

Early embryo development features autonomous, maternally-driven cell divisions that self- organize the multicellular blastula or blastocyst tissue. Maternal control cedes to the zygote starting with the onset of widespread zygotic genome activation (ZGA), which is essential for subsequent cell fate determination and morphogenesis. Intriguingly, although the onset of ZGA is highly regulated at the level of an embryo, it can be non-homogenous and precisely patterned at the single-cell level.

View Article and Find Full Text PDF

Steroid hormone-induced wingless ligands tune female intestinal size in Drosophila.

Nat Commun

January 2025

Department of Biology, Institute of Genetics, The Faculty of Mathematics and Natural Sciences, Heinrich Heine University Düsseldorf, Düsseldorf, Germany.

Female reproduction comes at great expense to energy metabolism compensated by extensive organ adaptations including intestinal size. Upon mating, endocrine signals orchestrate a 30% net increase of absorptive epithelium. Mating increases production of the steroid hormone Ecdysone released by the Drosophila ovaries that stimulates intestinal stem cell (ISC) divisions.

View Article and Find Full Text PDF

A templex-based study of the Atlantic Meridional Overturning Circulation dynamics in idealized chaotic models.

Chaos

January 2025

CNRS-IRD-CONICET-UBA, Institut Franco-Argentin d'Études sur le Climat et ses Impacts (IRL 3351 IFAECI), C1428EGA CABA, Argentina.

Significant changes in a system's dynamics can be understood through modifications in the topological structure of its flow in phase space. In the Earth's climate system, such changes are often referred to as tipping points. One of the large-scale components that may pass a tipping point is the Atlantic Meridional Overturning Circulation.

View Article and Find Full Text PDF

Want AI Summaries of new PubMed Abstracts delivered to your In-box?

Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!