Background Introduction Fractional Differential Equations (FDEs) extend traditional calculus by allowing derivatives and integrals of non-integer orders. This mathematical framework exhibits unique advantages in describing complex dynamical behaviors, particularly in the study of chaotic and nonlinear systems. Lyapunov Exponents (LEs) are critical ...
Academic Background In nonlinear dynamical systems, frequency switching has garnered significant attention in recent years due to its ubiquitous presence in the real world and its distinctive fast-slow dynamics. Frequency switching can induce divergence behaviors at certain switching thresholds, destabilizing bursting solutions in slowly excited ve...
The Influence of Double Delays in a Diffusive Predator-Prey System: A Study Using the Stability Switching Curve Method Academic Background The predator-prey model is one of the fundamental models in ecology for studying population interactions. Although these models may seem simple, they can generate complex dynamic structures and even lead to chao...
Research Background and Problem Introduction Nonlinear wave systems are core research topics in fields such as physics, optics, and condensed matter physics. However, real-world nonlinear wave systems are often subject to random noise interference, which can significantly alter the behavior of waves, such as soliton propagation, wave turbulence for...
In today’s era of information explosion, decision-makers are faced with a vast amount of information, not all of which is relevant to their decisions. To better make optimal decisions in data-rich environments, the Rational Inattention (RI) model has been introduced into the field of economics. The core idea of this model is that decision-makers ne...
Research Report on Identifying New Classes of Financial Price Jumps Using Wavelets Academic Background Price jumps in financial markets refer to significant price fluctuations occurring within an extremely short period, typically caused by exogenous factors (such as sudden news) or endogenous factors (internal market feedback mechanisms). Distingui...
Introduction In recent years, solving partial differential equations (PDEs) using numerical methods has played a significant role in various fields such as engineering and medicine. These methods have shown remarkable effectiveness in applications like topology and design optimization as well as clinical prognostication. However, the high computati...
A Research Report on a New Framework for Solving Migrant Resettlement Using Multiobjective Evolutionary Optimization Against the backdrop of accelerated globalization and evolving socio-economic conditions, migration has become an undeniable global trend. From the perspective of humanitarian relief or the sustainable development of a globalized eco...
New Results on Finite-Time Stability and Instability Theorems for Stochastic Nonlinear Time-Varying Systems 1. Research Background and Significance Stability theory is a central topic in systems theory and engineering applications, serving as the fundamental consideration in system analysis and synthesis. In stability theory, the two most commonly ...
Numerical Analysis Enhances Postoperative Visual Assessment and Optimization for Multifocal Intraocular Lenses (IOLs) Introduction and Research Background One of the main goals of cataract surgery is to achieve spectacle-free vision for patients. However, this goal is limited by two major challenges: loss of accommodative function and postoperative...