This study elucidates the ramifications of integrating a spatial fractional-order derivative into a diffusive mussel-algae model. While the formation in such models of patterns such as Turing instability, Hopf bifurcation, and Turing-Hopf bifurcation has been extensively scrutinized in prior investigations, the impact of spatial fractional-order derivatives remains largely unknown. Beyond its ecological significance, the fractional diffusion operator is of interest because it elicits novel and nontrivial pattern formations, particularly those emerging from Turing-Hopf bifurcations. Our core objective is to dissect how spatial fractional-order derivatives modulate the spatiotemporal dynamics... More >

Background: The possibility of an economic singularity---a finite‑time explosion of AI capability, financial capital, and inequality---has been discussed in futurist and economic literature, but endogenous feedback loops between AI, finance, and labour markets remain underexplored. Methods: This paper presents a dimensional reduction of a dynamical systems model of an economy with recursively self‑improving artificial intelligence and financial autocatalysis. By transforming to three economically meaningful ratios---financial depth per AI capability ($x = K_f/A$), AI capital per financial capital ($u = K_{ai}/K_f$), and employment odds ($z = L_p/(1-L_p)$)---the original four‑variable e... More >

This article investigates the finite-time boundedness (FTB) problem for a class of observer-based discrete linear time-varying networked control systems (DLTNCSs). The interval matrix method (IMM) is adopted to handle the bounded time-varying coefficient via an uncertain convex-hull representation, and a maximum absolute value method (MAM) is also established to solve the time-varying coefficient for comparison. An observer-based event-triggered controller (ETC) is then developed, and sufficient linear matrix inequality (LMI) conditions are derived to obtain the admissible controller gain. Moreover, an implementable algorithm is provided for minimizing the energy consumption. Two numerical e... More >

Chemotaxis, the directed movement of microorganisms in response to chemical gradients, plays a pivotal role in microbial ecology. This article provides a comprehensive review of mathematical models that couple chemotaxis with reaction dynamics to describe microbial population behavior. We discuss how such chemotaxis–reaction models capture essential ecological phenomena, from nutrient foraging and biofilm formation to inter-species competition and environmental processes. Key model formulations, starting from the classical Keller--Segel system, are presented alongside extensions incorporating multiple species, complex reaction terms, and fluid flow coupling. We survey rigorous mathematical... More >

This paper investigates the issue of prescribed-time mean-square synchronization (PTMSS) for stochastic coupled inertial neural networks (SCINNs), encompassing both scenarios without time delays (TDs) and with TDs. By constructing appropriate Lyapunov functionals and utilizing the prescribed-time stability (PTS) approach, combined with the theory of directed spanning trees, several sufficient conditions are rigorously derived to realize the prescribed-time mean-square synchronization within a given time $t_p$ for SCINNs with and without TDs. Different from most existing results that primarily address deterministic systems or neglect stochastic disturbances and time delays, this work explicit... More >