Search · four archives
Search · four archives
23 papers · ranked by Valyu relevance
Brahim Benhammouda, Hector Vazquez-Leal
This work presents an analytical solution of some nonlinear delay differential equations (DDEs) with variable delays. Such DDEs are difficult to treat numerically and cannot be solved by existing general purpose codes. A new method of steps combined with the differential transform method (DTM) is proposed as a powerful…
David S. Glass, Xiaofan Jin, Ingmar H. Riedel-Kruse
Biological regulatory systems, such as transcription factor or kinase networks, consist of complex dynamical interactions among many components. “Network motif” models focus on small sub-networks to provide quantitative insight into overall behavior. However, conventional network motif models often ignore time delays…
Andrei D. Polyanin
nonlinear PDEs and delay PDEs Authors: ['Andrei D. Polyanin'] Using the principle of structural analogy of solutions, approaches have been developed for constructing exact solutions of complex nonlinear PDEs, including PDEs with delay, based on the use of special solutions to auxiliary simpler related equations. It is…
Bogdan Căruntu, Constantin Bota
We use the polynomial least squares method (PLSM), which allows us to compute analytical approximate polynomial solutions for a very general class of strongly nonlinear delay differential equations. The method is tested by computing approximate solutions for several applications including the pantograph equations and a…
Leping Sun
This paper is concerned with the backward differential formula or BDF methods for a class of nonlinear 2-delay differential algebraic equations. We obtain two sufficient conditions under which the methods are stable and asymptotically stable. At last, examples show that our methods are true.
Mathew O. Aibinu, Surendra Thakur, Sibusiso Moyo
A technique which is known as Sumudu Transform Method (STM) is studied for the construction of solutions of a most general form of delay differential equations of pantograph type. This is a pioneer study on using the STM to construct the solutions of delay differential equations of pantograph type with variable…
Authors not listed
with both positive and negative terms and time-variable delays. Our results improve and generalize several existing criteria available in the literature that address restricted cases, such as constant delays or the absence of negative coefficients. Under additional assumptions on slowly varying parameters, we derive…
Rohul Amin, Shah Nazir, Iván García-Magariño
Wireless sensor network and industrial internet of things have been a growing area of research which is exploited in various fields such as smart home, smart industries, smart transportation, and so on. There is a need of a mechanism which can easily tackle the problems of nonlinear delay integro-differential equations…
Mathew O. Aibinu, Surendra Thakur, Sibusiso Moyo
a Institute for Systems Science & KZN E-Skill CoLab, Durban University of Technology, Durban 4000, South Africa bDSI-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS), South Africa cNational Institute for Theoretical and Computational Sciences (NITheCS), South Africa dKZN E-Skill CoLab…
Mark A. Pinsky
Instability of Some Nonlinear Systems with Delays and Variable Coefficients Authors: ['Mark A. Pinsky'] Abstract. This paper presents a novel methodology for evaluating the boundedness, stability, and instability of some vector nonlinear systems with multiple time-varying delays and variable coefficients. The proposed…
Dario Schöbi, Cao-Tri Do, Stefan Frässle, Marc Tittgemeyer + 2 more
Dynamic causal models (DCMs) of electrophysiological data allow, in principle, for inference on hidden, bulk synaptic function in neural circuits. The directed influences between the neuronal elements of modeled circuits are subject to delays due to the finite transmission speed of axonal connections. Ordinary…
Dongmei Xia, Kaiyuan Chen, Lin Sun, Guojin Qin
This study delves into neutral-type systems (NTSs), emphasizing the critical role of defining precise reachable set (RS) boundaries for safe and efficient system design and operation. The investigation notably addresses the challenges posed by time-varying delays, applying Lyapunov’s direct method alongside advanced…
Mark A. Pinsky
and Stability Analysis Authors: ['Mark A. Pinsky'] Abstract. This paper introduces a new method for assessing the boundedness and stability of certain vector nonlinear systems with delays and variable coefficients. The approach is based on developing scalar counterparts to the given vector systems. We prove that the…
Daniel Sepúlveda
We study approximation of non-autonomous linear differential equations with variable delay over infinite intervals. We use piecewise constant argument to obtain a corresponding discrete difference equation. The study of numerical approximation over an unbounded interval is in correspondence with the problem of…
Bartosz Prokop, Lendert Gelens
Periodic changes in the concentration or activity of different molecules regulate vital cellular processes such as cell division and circadian rhythms. Developing mathematical models is essential to better understand the mechanisms underlying these oscillations. Recent data-driven methods like SINDy have fundamentally…
Li Zuo, Fengtai Mei
Since the nonlinear parabolic equation has many variables, its calculation process is mostly an algebraic operation, which makes it difficult to express the discrete process concisely, which makes it difficult to effectively solve the two grid algorithm problems and the convergence problem of reaction diffusion. The…
D. T. Pham, Z. E. Musielak
Non-standard Lagrangians do not display any discernible energy-like terms, yet they give the same equations of motion as standard Lagrangians, which have easily identifiable energy-like terms. A new method to derive non-standard Lagrangians for second-order nonlinear differential equations with damping is developed and…
Germán Abrevaya, Aleksandr Aravkin, Guillermo Cecchi, Irina Rish + 3 more
Many real-world data sets, especially in biology, are produced by highly multivariate and nonlinear complex dynamical systems. In this paper, we focus on brain imaging data, including both calcium imaging and functional MRI data. Standard vector-autoregressive models are limited by their linearity assumptions, while…
Justin Eilertsen, Wylie Stroberg, Santiago Schnell
A theoretical analysis is performed on the nonlinear ordinary differential equations that govern the dynamics of a coupled enzyme catalyzed reaction. The assay consists of a non-observable reaction and an indicator (observable) reaction, where the product of the first reaction is the enzyme for the second. Both…
Authors not listed
We develop a control-oriented model for manipulating calcium carbonate (CaCO3) precipitation through pH and/or dissolved CO2(aq) adjustments in a semi-batch process. We present two open-loop control strategies: first, a closed-form optimal control solution derived via Pontryagin’s Minimum Principle; and second, an…
Marta Leocata, J. C. L. Alfonso, Nikos I. Kavallaris, Haralampos Hatzikirou
Typically stochastic differential equations (SDEs) involve an additive or multiplicative noise term. Here, we are interested in stochastic differential equations for which the white noise is non-linearly integrated in the corresponding evolution term, typically termed as random ordinary differential equations (RODEs).…
Justin Eilertsen, Wylie Stroberg, Santiago Schnell
A theoretical analysis is performed on the nonlinear ordinary differential equations that govern the dynamics of a reaction mechanism of zymogen activation. The reaction consists of a primary non-observable zymogen activation reaction that it is coupled to an indicator (observable) reaction. The product of the first…
Justin Eilertsen, Wylie Stroberg, Santiago Schnell
The determination of a substrate or enzyme activity by coupling of one enzymatic reaction with another easily detectable (indicator) reaction is a common practice in the biochemical sciences. Usually, the kinetics of enzyme reactions is simplified with singular perturbation analysis to derive rate or time course…