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 >

This study examines the problem of decentralized non-fragile dissipative control for a category of fractional-order linear uncertain large-scale systems. We assume that the subsystems uncertainty is norm-bounded and time-varying. Furthermore, we assume that the state-feedback gains for subsystems of the fractional-order large-scale system have norm-bounded controller gain variations. To achieve our goal, we introduce the concept of $(S, Q, R)-$dissipativity for fractional-order interconnected systems. By using this definition and mathematical transformations with fractional calculus, a decentralized non-fragile state-feedback controller is designed so that the closed-loop interconnected sys... More >

A kind of discrete-time singular predator-prey system with time-varying harvesting term is investigated. By using theory of singular systems, bifurcation and center manifold theory, the stability and Neimark-Sacker bifurcation of such system is studied, and some conditions are used to judge local stability of its fixed points and ensure existence of the Neimark-Sacker bifurcation for the proposed discrete-time singular system are derived. Finally, numerical simulations are given to show the obtained results. The results of the paper complements some previous works, and we believe that the method of this paper can be used to study bifurcation for other discrete-time complex singular systems. More >

In this paper, we develop a mathematical model for juvenile delinquency transmission dynamics by incorporating key control strategies, namely precautionary measures, public education, and intervention programs. The model aims to identify effective prevention and control measures for curbing the spread of delinquent behavior among youths, with particular emphasis on evaluating the efficacy of public education. Adopting an epidemiological modelling framework, we derive a system of nonlinear differential equations governing the dynamics of juvenile delinquency over time. Stability analysis of the model is conducted, and the basic reproduction number along with the equilibrium points for both de... More >

This paper investigates fixed-time stability of delayed nonlinear dynamic systems. At first, by designing an inequality with sigmoid-function, a new kind of fixed-time stability lemma is constructed. Then, as an application, the new proposed lemma is applied to discuss fixed-time stabilization(FT) for a kind of delayed neural networks. At last, simulations are also given to show the effectiveness of the derived results. More >