We introduce a mathematical model on the dynamics of demand and supply incorporating collectability and saturation factors. Our analysis shows that when the fluctuation of the determinants of demand and supply is strong enough, there is chaos in the demand-supply dynamics. Our numerical simulation shows that such a chaos is not an attractor (i.e. dynamics is not approaching the chaos), instead ...

We study the limit as α → 0+ of the long-time dynamics for various approximate α-models of a viscous incompressible fluid and their connection with the trajectory attractor of the exact 3D Navier-Stokes system. The α-models under consideration are divided into two classes depending on the orthogonality properties of the nonlinear terms of the equations generating every particular α-model. We sh...

The capacity for flexible sensory-action association in animals has been related to context-dependent attractor dynamics outside the sensory cortices. Here, we report a line of evidence that flexibly modulated attractor dynamics during task switching are already present in the higher visual cortex in macaque monkeys. With a nonlinear decoding approach, we can extract the particular aspect of th...

The Boolean network can be used as a mathematical model for gene regulatory networks. An attractor, which is a state of a Boolean network repeating itself periodically, can represent a stable stage of a gene regulatory network. It is known that the problem of finding an attractor of the shortest period is NP-hard. In this article, we give a fixed-parameter algorithm for detecting a singleton at...

This study examined rhythmic finger movements in the steady state and when momentarily perturbed in order to derive their qualitative dynamical properties. Movement frequency, amplitude, and peak velocity were stable under perturbation, signaling the presence of an attractor, and the topological dimensionality of that attractor was approximately equal to one. The strength of the attractor was c...

We model an elastic beam subject to a contact load which displaces under a chaotic external forcing, motivated by application of a ship carrying either a crane, or fluids in internal tanks. This model not only has rich dynamics and relevance in its own right, it gives rise to a Partial Differential Equation (PDE) whose solutions are chaotic, with an attractor whose points lie “near” a low-dimen...