Related papers: Positive Equilibria of Hill-Type Kinetic Systems
Muscle contraction is a prototypical multiscale chemomechanical process in which ATP hydrolysis at the molecular level drives force generation and mechanical work at larger scales. A long-standing challenge is to connect microscopic…
Kernel-based learning methods can dramatically increase the storage capacity of Hopfield networks, yet the dynamical mechanisms behind this enhancement remain poorly understood. We address this gap by combining a geometric characterization…
In this letter we introduce a class of delayed kinetic systems derived from mass action type reaction network models. We define the time delayed positive stoichiometric compatibility classes and the notion of complex balanced time delayed…
Networks with absolute concentration robustness (ACR) have the property that a translation of a coordinate hyperplane either contains all steady states (static ACR) or attracts all trajectories (dynamic ACR). The implication for the…
We consider delayed chemical reaction networks with generalized kinetics of product form and show that complex balancing implies that within each positive stoichiometric compatibility class there is a unique positive equilibrium that is…
In this work we present a new class of real scalar field models admitting strongly interactive kink solutions. Instead of the usual exponential asymptotic behavior these topological solutions exhibit a power-law one. We investigate the…
Very often, models in biology, chemistry, physics, and engineering are systems of polynomial or power-law ordinary differential equations, arising from a reaction network. Such dynamical systems can be generated by many different reaction…
This paper studies the relations among system parameters, uniqueness, and stability of equilibria, for kinetic systems given in the form of polynomial ODEs. Such models are commonly used to describe the dynamics of nonnegative systems, with…
Absolute concentration robustness (ACR) and concordance are novel concepts in the theory of robustness and stability within Chemical Reaction Network Theory. In this paper, we have extended Shinar and Feinberg's reaction network analysis…
We present a kinetic theory for inhomogeneous systems with weak long-range interactions. Starting from the Klimontovich equation and using a quasilinear theory, we obtain a closed kinetic equation describing the relaxation of the…
Chemical reaction network theory is a powerful framework to describe and analyze chemical systems. While much about the concentration profile in an equilibrium state can be determined in terms of the graph structure, the overall reaction's…
Motivation: A Chemical Reaction Network (CRN) is a set of chemical reactions, which can be very complex and difficult to analyze. Indeed, dynamical properties of CRNs can be described by a set of non-linear differential equations that…
We develop a new method for proving hypocoercivity for a large class of linear kinetic equations with only one conservation law. Local mass conservation is assumed at the level of the collision kernel, while transport involves a confining…
In this paper, we study various theoretical properties of a class of prioritized inverse kinematics (PIK) solutions that can be considered as a class of (output regulation or tracking) control laws of a dynamical system with prioritized…
We derive an energy bound for inertial Hegselmann-Krause (HK) systems, which we define as a variant of the classic HK model in which the agents can change their weights arbitrarily at each step. We use the bound to prove the convergence of…
We complete the existing literature on the kinetic theory of systems with long-range interactions. Starting from the BBGKY hierarchy, or using projection operator technics or a quasilinear theory, a general kinetic equation can be derived…
This review concerns recent results on the quantitative study of convergence towards the stationary state for spatially inhomogeneous kinetic equations. We focus on analytical results obtained by means of certain probabilistic techniques…
Two networks are said to be linearly conjugate if the solution of their dynamic equations can be transformed into each other by a positive linear transformation. The study on dynamical equivalence in chemical kinetic systems was initiated…
Complex biochemical pathways or regulatory enzyme kinetics can be reduced to chains of elementary reactions, which can be described in terms of chemical kinetics. This discipline provides a set of tools for quantifying and understanding the…
Living systems maintain stable internal states despite environmental fluctuations. Absolute concentration robustness (ACR) is a striking homeostatic phenomenon in which the steady-state concentration of a species remains invariant despite…