DOI: 0804.0248Apr 2, 2008Paper

Competition between transients in the rate of approach to a fixed point

ArXiv
Judy DayCarson C Chow

Abstract

Dynamical systems studies of differential equations often focus on the behavior of solutions near critical points and on invariant manifolds, to elucidate the organization of the associated flow. In addition, effective methods, such as the use of Poincare maps and phase resetting curves, have been developed for the study of periodic orbits. However, the analysis of transient dynamics associated with solutions on their way to an attracting fixed point has not received much rigorous attention. This paper introduces methods for the study of such transient dynamics. In particular, we focus on the analysis of whether one component of a solution to a system of differential equations can overtake the corresponding component of a reference solution, given that both solutions approach the same stable node. We call this phenomenon tolerance, which derives from a certain biological effect. Here, we establish certain general conditions, based on the initial conditions associated with the two solutions and the properties of the vector field, that guarantee that tolerance does or does not occur in two-dimensional systems. We illustrate these conditions in particular examples, and we derive and demonstrate additional techniques that can be ...Continue Reading

Related Concepts

Trending Feeds

COVID-19

Coronaviruses encompass a large family of viruses that cause the common cold as well as more serious diseases, such as the ongoing outbreak of coronavirus disease 2019 (COVID-19; formally known as 2019-nCoV). Coronaviruses can spread from animals to humans; symptoms include fever, cough, shortness of breath, and breathing difficulties; in more severe cases, infection can lead to death. This feed covers recent research on COVID-19.

Hereditary Sensory Autonomic Neuropathy

Hereditary Sensory Autonomic Neuropathies are a group of inherited neurodegenerative disorders characterized clinically by loss of sensation and autonomic dysfunction. Here is the latest research on these neuropathies.

Evolution of Pluripotency

Pluripotency refers to the ability of a cell to develop into three primary germ cell layers of the embryo. This feed focuses on the mechanisms that underlie the evolution of pluripotency. Here is the latest research.

Chronic Fatigue Syndrome

Chronic fatigue syndrome is a disease characterized by unexplained disabling fatigue; the pathology of which is incompletely understood. Discover the latest research on chronic fatigue syndrome here.

Nuclear Pore Complex in ALS/FTD

Alterations in nucleocytoplasmic transport, controlled by the nuclear pore complex, may be involved in the pathomechanism underlying multiple neurodegenerative diseases including Amyotrophic Lateral Sclerosis and Frontotemporal Dementia. Here is the latest research on the nuclear pore complex in ALS and FTD.

Landau-Kleffner Syndrome

Landau Kleffner syndrome (LKS), also called infantile acquired aphasia, acquired epileptic aphasia, or aphasia with convulsive disorder, is a rare childhood neurological syndrome characterized by the sudden or gradual development of aphasia (the inability to understand or express language) and an abnormal electroencephalogram. Discover the latest research on LKS here.

STING Receptor Agonists

Stimulator of IFN genes (STING) are a group of transmembrane proteins that are involved in the induction of type I interferon that is important in the innate immune response. The stimulation of STING has been an active area of research in the treatment of cancer and infectious diseases. Here is the latest research on STING receptor agonists.

Microbicide

Microbicides are products that can be applied to vaginal or rectal mucosal surfaces with the goal of preventing, or at least significantly reducing, the transmission of sexually transmitted infections. Here is the latest research on microbicides.

Regulation of Vocal-Motor Plasticity

Dopaminergic projections to the basal ganglia and nucleus accumbens shape the learning and plasticity of motivated behaviors across species including the regulation of vocal-motor plasticity and performance in songbirds. Discover the latest research on the regulation of vocal-motor plasticity here.

Related Papers

SIAM Journal on Applied Dynamical Systems
Judy DayCarson C Chow
Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
Bruce M BoghosianPeter V Coveney
Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
V N BelykhM Hasler
© 2021 Meta ULC. All rights reserved