Search · four archives
Search · four archives
20 papers · ranked by Valyu relevance
Yu Zhang, Longsuo Li
In this paper, we concern stability of numerical methods applied to stochastic delay integro-differential equations. For linear stochastic delay integro-differential equations, it is shown that the mean-square stability is derived by the split-step backward Euler method without any restriction on step-size, while the…
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…
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…
Kenta Nakata, Ken‐ichi Maruno
We propose a systematic method for constructing integrable delay-difference and delay-differential analogues of known soliton equations such as the Lotka-Volterra, Toda lattice, and sine-Gordon equations and their multi-soliton solutions. It is carried out by applying a reduction and delay-differential limit to the…
В. А. Дородницын, R. V. Kozlov, Sergey V. Meleshko
A Lagrangian formalism for variational second-order delay ordinary differential equations (DODEs) is developed. The Noether operator identity for a DODE is established, which relates the invariance of a Lagrangian function with the appropriate variational equations and the conserved quantities. The identity is used to…
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…
Shuo-Tsung Chen, Shun‐Pin Hsu, Huang‐Nan Huang, Binyan Yang
In this work, we establish the response of scalar systems with multiple discrete delays based on the Laplace transform. The time response function is expressed as the sum of infinite series of exponentials acting on eigenvalues inside countable branches of the Lambert W functions. Eigenvalues in each branch of Lambert…
Chavda Divyesh Vinodbhai, Shruti Dubey
In this paper, an efficient orthogonal neural network (ONN) approach is introduced to solve the higher-order neutral delay differential equations (NDDEs) with variable coefficients and multiple delays. The method is implemented by replacing the hidden layer of the feed-forward neural network with the orthogonal…
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.
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…
Sachin Bhalekar, Deepa Gupta
one can have a critical value of α viz α∗ such that the system is stable for 0 < α < α∗ and unstable for α∗ < α ≤ 1. In general, if such system is stable for some α0 ∈ (0, 1) then it remains stable for all α < α0.
Gemeda Tolessa Lubo, Gemechis File Duressa
Objectives The main aim of this paper is to develop a linear B-spline finite element method for solving generalized diffusion equations with delay. The linear B-spline basis function is used to discretize the space variable. The time discretization process is based on Crank-Nicolson. The benefit of the scheme is that…
Jayvant Patade, Sachin Bhalekar
Proportional delay is a particular case of time dependent delay. In this article, we consider differential equations involving multiple delays. The series solution of this equation leads to a class of special functions. This class of special functions is independent from all the existing special functions obtained as a…
Yukihiko Nakata
has a periodic solution of period two for r > π 2 (when the steady state, x = 1, is unstable). In order to find the periodic solution, we study an integrable system of ordinary differential equations, following the idea by Kaplan and Yorke [14]. The periodic solution is expressed in terms of the Jacobi elliptic…
Andrei D. Polyanin, Alexei I. Zhurov
where u = u(x, t), w = u(x, t−τ), and τ is the delay time. The method is based on searching for solutions in the form u = PN n=1 ξn(x)ηn(t), where the functions ξn(x) and ηn(t) are determined from additional functional constraints (which are difference or functional equations) and the original delay partial…
Vanessa Steindorf, Sergio Oliva, Jianhong Wu
Dengue fever is endemic in tropical and sub-tropical countries, and some of the important features of Dengue fever spread continues to pose challenges for mathematical modelling. Here, we propose a system of integro-differential equations (IDE) to study the disease transmission dynamics that involves multiserotypes and…
Quanmin Zhu, Jianhua Zhang, Weicun Zhang, José María Amigó
This study presents a general framework for the control of unknown dynamic systems with unknown input delay. A concise output feedback control system is structured with tuning stabilization/dynamic response by an output feedback low gain, removing steady state error against step reference with a feedforward gain. A…
A.V. Paraskevov, T.S. Zemskova
The classical biophysical Morris-Lecar model of neuronal excitability predicts that upon stimulation of the neuron with a sufficiently large constant depolarizing current there exists a finite interval of the current values where periodic spike generation occurs. Above the upper boundary of this interval there is a…
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
This work investigates the fluid dynamics of electrolyte mixing within the tanks of vanadium flow batteries. Custom axisymmetric tanks are used to study the different flow regimes that emerge during battery cycling at various flow rates. A dual online diagnostic tool based on UV-vis spectroscopy enables precise…