动力系统
We investigate the dynamics of the AM2 model in a serial configuration of two interconnected chemostats with distinct dilution rates. The system is described by nonlinear differential equations, for which the usual reduction from an…
Let $s > 1$ be a large integer, and let $f$ be a diffeomorphism sufficiently close in the $C^{s}$-topology to the time-1 map of a $C^{s}$ generic volume-preserving Anosov flow on a $3$-dimensional compact manifold. We show that for any…
We investigate consensus formation and flocking behavior in multi-agent systems subject to two distinct types of delays: a transmission delay accounting for information exchange between agents, and a reaction delay representing the…
We extend a three-stage anaerobic digestion model by incorporating microbial mortality into the hydrolysis of particulate organic matter. The model describes hydrolysis, acidogenesis, and methanogenesis, each with distinct dilution and…
This paper develops a transfer operator framework for stochastic hybrid systems with guard-induced resets, encompassing both the Koopman and Frobenius--Perron operators. Exploiting their duality, we derive a unified formulation in which…
We introduce and analyze a class of neural network models motivated by the Drosophila central complex nervous system, designed to capture the emergence and dynamics of orientation-selective activity bumps. Starting from a biologically…
We study the sequence entropy of rank one measure-preserving systems along subexponential sequences. We prove that the sequence entropy along a large class of sequences can be infinite using Ornstein's probabilistic constructions. Moreover,…
We survey recent results and current challenges concerning the growth rate inequality for sphere endomorphisms, and present a number of open problems and conjectures arising in this context.
In 2002, Kamae and Zamboni introduced maximal pattern complexity and determined that any aperiodic sequence must have maximal pattern complexity at least $2k$. In 2006, Kamae and Rao examined the maximal pattern complexity of sequences over…
In this manuscript, we construct an explicit counterexample of a smooth \(C^{\infty}\), periodic dynamical system on the torus \(\mathbb{T}^3\) for which the rotation vector exists in a weak sense, but fails to exist in the strong sense of…
In this paper, we deal with the classification complexity of continuous (Devaney) chaotic systems in dimensions $0,1$ and $\infty$ using the framework of invariant descriptive set theory. We identify the complexity in dimensions $0$ and…
We shall describe a new construction of equilibrium states for a class of partially hyperbolic systems. This generalises our construction for Gibbs measures in the uniformly hyperbolic setting. This more general setting introduces new…
In this paper, we mathematically describe the time evolution of protein folding features via Iori et al.'s heteropolymer model. More specifically, we identify that the folding amino acid chain evolve according to a power law $D \sim…
We show that every free continuous action of a countably infinite elementary amenable group on a finite-dimensional compact metrizable space is almost finite. As a consequence, the crossed products of minimal such actions are…
We prove a centre manifold theorem for a map along a manifold-with-boundary of fixed points, and provide an application to the study of gradient descent with large step size on two-layer matrix factorisation problems.
We consider a generalized Takagi function for beta-expansions with the base $1<\beta\leq2$, motivated by multifractal analysis for digit frequency sets of beta-expansions [20]. We show that it is pointwise $\alpha$-H\"older continuous for…
We develop a qualitative-dynamics framework for general Iterated Function Systems (IFSs) on locally compact spaces. Our approach extends to IFSs a framework recently developed in the semiflows setting by James Yorke and the present author…
This paper investigates the statistical properties of random open dynamical systems generated by families of Lasota--Yorke maps. Open systems, in which trajectories may escape through `holes', model transient phenomena and present…
A standard organization of production lines exhibiting self-balancing behavior is given by bucket brigades. Their study in operations research was initiated by the foundational work of Bartholdi and Eisenstein ({\em Operations Research},…
We study conditions for the well-posedness of nonautonomous perturbation of evolution equations of the form \[ u'(t)=(A+B(t))u(t), \quad t \in [a,b], \] where $A$ generates a $\mathrm{C}_0$-semigroup $\left (T(t)\right )_{t\ge 0}$ with $\|…