Search · four archives
Search · four archives
20 papers · ranked by Valyu relevance
Mark A. Pinsky
— Existing methods rarely capture the temporal evolution of solution norms in vector nonlinear DDEs with variable delays and coefficients, often leading to overly conservative boundedness and stability criteria. We develop a framework that constructs scalar counterparts of vector DDEs whose solutions upper-bound the…
Leonid Berezansky, Elena Braverman, Oleg Kupervasser
Linearised equations for known mathematical models have different forms: equations with one, two or several delays, equations in which all the terms are delayed and those containing a non-delay term, dominating or not, equations with only nonnegative coefficients or equations with oscillatory coefficients, equations…
Stone Yao, Vipin Kumar, Roberto Guglielmi
In this paper we propose a novel physics-informed neural network framework for solving general first-order delay differential equations. Our approach combines a differentiable history switch, a trial-solution formulation that explicitly enforces history constraints, and a segmented collocation strategy to stabilize…
Mark A. Pinsky
Stability and boundedness analysis for vector nonlinear systems with variable delays and coefficients remains challenging due to the conservatism of existing methods. Moreover, estimates of the transient behavior of solution norms remain insufficiently developed. This paper presents an approach to estimate the temporal…
H. A. A. El-Saka, D. El. A. El-Sherbeny, A. M. A. El-Sayed
In this paper, we analyze the stability of the fractional distributed delay models. We use the linear chain trick to convert these models into an incommensurate fractional order systems. We get the stability regions by studying the characteristic equation around equilibrium points. We investigate how the fractional…
Vasyl Martsenyuk, Tomasz Gancarczyk, Tiziano Squartini
Understanding how information spreads in complex networks is essential for analyzing social influence, opinion formation, and the emergence of collective behavior. In many real-world systems, interactions are not instantaneous but involve delays due to communication, cognition, and response times. Motivated by this…
Khadija Shakeel, Dumitru Baleanu, Muhammad Abbas, Majeed Ahmad Yousif + 3 more
This study introduces new exact soliton solutions of the time-fractional Joseph-Egri equation by employing the Tanh-Coth and Jacobi Elliptic Function methods. Using Jumarie’s modified Riemann-Liouville derivative, a wide variety of soliton structures-such as periodic, bell-shaped, W-shaped, kink, and anti-bell-shaped…
Yiming Cheng, Yan Li
Chimeric antigen receptor (CAR) T-cell therapies undergo rapid in vivo expansion followed by contraction and variable long-term persistence after a single infusion, yielding cellular kinetic (CK) profiles that differ fundamentally from conventional small-molecule and biologic pharmacokinetics. Piecewise, phase-based CK…
Ivanka Stamova, Gani Stamov, Cvetelina Spirova, José F.F. Mendes
The focus of this research is the qualitative behavior of a reaction-diffusion neural network with distributed delays and conformable derivatives under impulsive perturbations. In particular, the almost periodic behavior of the proposed model is studied using a Lyapunov-based approach. By constructing an appropriate…
Nimai Sarkar, Mausumi Sen
This paper studies the transmission dynamics of influenza by using a fractional SIR (Susceptible-Infected-Removed) epidemic model with discrete delay to describe the short-term dynamics. The model includes history-dependent effects through Caputo fractional derivative and maturity delays, which are biologically…
Polyanin, Andrei D.
The paper deals with nonlinear Schr¨odinger equations of the general form, depending on time and two spatial variables, the potential and dispersion of which are specified by one or two arbitrary functions. The equations under consideration naturally generalize a number of related nonlinear partial differential…
Leonardo Demarchi
Although many animals rely on visual information to navigate, optic flow is inherently ambiguous as it confounds information about motion speed and object distance. As a result, the visual feedback produced by a given motor command is context-dependent and requires an appropriately adapted response. Recent experiments…
Jie Deng, Xinyu Zhang, Xuchang Zhang, Xing Yang
Coupled diffusion–reaction partial differential equations (PDEs) describe biochemical network dynamics but are difficult to solve for realistic multi-species systems without combining mechanism and data. We present a multi-stage physics-informed neural network (PINN) for multi-species diffusion–reaction PDEs and apply…
Mohammed S. Mechee, Mohammed Mahmood Salih
Background In this paper, we focus on deriving an efficient method for solving ordinary differential equations (ODEs) of sixth order, and then, we modify the proposed method for solving fractional differential equations (FDEs). Methods The methodology of this paper used the approach of derivation of implicit numerical…
Authors not listed
Accurate modeling of drug concentration--time (C--t) profiles is central to pharmacokinetics (PK) and plays a critical role in both early-stage compound selection and late-stage individualized dosing. Traditional PK model offer mechanistic interpretability but often rely on rigid assumptions, extensive…
Lei Ren, Shixin Jin, António M. Lopes
This paper introduces a novel approach using physics-informed neural networks (PINNs) to simultaneously solve variable-order time fractional diffusion equations and infer the time-dependent fractional order from data. By embedding the governing equations into the neural network’s loss function, our method achieves high…
Zhiwei Zhang, Shuwang Li, John Lowengrub, Steven M. Wise
We present a fast, unconditionally energy-stable numerical scheme for simulating vesicle deformation under osmotic pressure using a phase-field approach. The model couples an Allen–Cahn equation for the biomembrane interface with a variable-mobility Cahn–Hilliard equation governing mass exchange across the membrane.…
Mika Ohkawa, Ying Joey Zhou, Saskia Haegens, Matin Jafarian
Learning new information in the presence of distracters and changing conditions requires the ability to adapt. In the brain, this adaptive capability has been linked to dynamic interactions between attention and working memory, which enable the selective filtering of irrelevant input while preserving behaviorally…
Denizhan Pak, Randall D. Beer
Organisms must manage a trade-off between robustness and flexibility as they enact adaptive behaviors. One way organisms achieve this is by navigating a network of quasi-stable behavioral states. Evidence for such behavioral states has been observed in many organisms, and new methods for detecting these states have…
Navid Akbari, Kai Mason, Aaron Gruber, Wilten Nicola
Spiking Neural Networks (SNNs) have the potential to replicate the brain’s computational efficacy by explicitly incorporating action potentials or “spikes”, which is not a feature of most artificial neural networks. However, training SNNs is difficult due to the non-differentiable nature of the most common spiking…