In this letter, the fixed-time stabilization of a class of dynamical systems is investigated. By using a fixed-time stability lemma and feedback control, new algebraic criteria ensuring the fixed-time stabilization of the dynamical systems under consideration are established. The obtained results are then applied to stabilize a chaotic system, and numerical simulations demonstrate the effectiveness of the theoretical results. More >

We study a geometrically defined return map associated with domains in the class $\mathcal O_C$, where a fixed convex core $C\subset\mathbb R^N$ is linked to the outer boundary $\partial\Omega$ through outward normal rays and a thickness function $d:\partial C\to(0,\infty)$. The radial map $\Phi(c)=c+d(c)\nu(c)$ is combined with a reciprocal map that follows the inward normal to $\partial\Omega$ back to its first intersection with the convex core. Their composition $F=\pi\circ\Phi:\partial C\to\partial C$ defines a geometrically generated discrete dynamical system on $\partial C$. Using the exact normal geometry of the radial parametrization, we derive the local quadratic-remainder formula $... More >

This study develops a treatment-modulated discrete framework for breast-tumor dynamics, emphasizing dimensional consistency, treatment dependence, and the distinction between scalar tumor burden and spatial tumor-density fields. Starting from the dimensional logistic growth law, treatment is introduced through a cycle-dependent survival factor. Normalization by the continuous carrying capacity $K_c$ yields the exact Euler update $y_{n+1}=S_n[y_n+g\Delta t_n y_n(1-y_n)]$, whereas the canonical non-autonomous map $x_{n+1}=r_nx_n(1-x_n)$, with $r_n=(1+g\Delta t_n)S_n$, is retained as a reduced nonlinear benchmark. This distinction prevents discretization-induced period-doubling and chaos from b... More >

Artificial intelligence (AI) investment, environmental, social, and governance (ESG) disclosure, and green supply chain collaboration increasingly operate as an interconnected corporate sustainability system, yet their relationships are commonly examined through static or approximately linear models. This study develops a bounded three-dimensional discrete nonlinear framework in which firms periodically adjust AI-investment maturity, ESG disclosure quality, and green supply chain collaboration in response to cross-domain benefits and self-limiting organizational costs. The model contributes by separating structural complementarity from organizational responsiveness, allowing the same long-ru... More >

This paper develops a third-order fully implicit adaptive variable step-size superclass block backward differentiation formula (VSBBDF3) for the efficient numerical simulation of nonlinear stiff dynamical systems, including oscillatory, chaotic, and reaction-kinetics systems governed by ordinary differential equations. The method extends the classical block BDF framework through a structured superclass coefficient formulation while preserving full implicitness. By computing multiple solution approximations simultaneously within each block, the scheme enhances both stability and computational efficiency. An adaptive step-size strategy controls local truncation errors, enabling dynamic respons... More >

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 >