Related papers: Implicit function theorem for nonlinear time-delay…
In this note, analysis of time delay systems using Lambert W function approach is reassessed. A common canonical form of time delay systems is defined. We extended the recent results of [6] for second order into nth order system. The…
This paper introduces an algorithm for discovering implicit and delayed causal relations between events observed by a robot at arbitrary times, with the objective of improving data-efficiency and interpretability of model-based…
Partial differential equations with discrete (concentrated) state-dependent delays in the space of continuous functions are investigated. In general, the corresponding initial value problem is not well posed, so we find an additional…
Real-world dynamical systems with retardation effects are described in general not by a single, precisely defined time delay, but by a range of delay times. An exact mapping onto a set of $N+1$ ordinary differential equations exists when…
Delay differential equations are of great importance in science, engineering, medicine and biological models. These type of models include time delay phenomena which is helpful for characterising the real-world applications in machine…
Ou et al. (2022) introduce the problem of learning set functions from data generated by a so-called optimal subset oracle. Their approach approximates the underlying utility function with an energy-based model, whose parameters are…
The celebrated Takens' embedding theorem provides a theoretical foundation for reconstructing the full state of a dynamical system from partial observations. However, the classical theorem assumes that the underlying system is deterministic…
Long-term memory is a feature observed in systems ranging from neural networks to epidemiological models. The memory in such systems is usually modeled by the time delay. Furthermore, the nonlocal operators, such as the "fractional order…
This paper continues the study of [11, 13] for stationary solutions of stochastic linear retarded functional differential equations with the emphasis on delays which appear in those terms including spatial partial derivatives. As a…
A system of inhomogeneous second-order difference equations with linear parts given by noncommutative matrix coefficients are considered. Closed form of its solution is derived by means of newly defined delayed matrix sine/cosine using the…
Bifurcation equations, non-degeneracy and transversality conditions are obtained for the fold, transcritical, pitchfork and flip bifurcations for periodic points of one dimensional implicitly defined discrete dynamical systems. The backward…
Time-invariant finite-dimensional systems, under reasonable continuity assumptions, exhibit the property that if solutions exist for all future times, the set of vectors reachable from a bounded set of initial conditions over bounded time…
In this paper we derive the equations of motion for nonholonomic systems subject to inequality constraints, both, in continuous-time and discrete-time. The last is done by discretizing the continuous time-variational principle which defined…
The Implicit and Inverse Function Theorems are special cases of a general Implicit/Inverse Function Theorem which can be easily derived from either theorem. The theorems can thus be easily deduced from each other via the generalized…
Fast and accurate solutions of time-dependent partial differential equations (PDEs) are of pivotal interest to many research fields, including physics, engineering, and biology. Generally, implicit/semi-implicit schemes are preferred over…
This article proposes modifications of the Parareal algorithm for its application to higher index differential algebraic equations (DAEs). It is based on the idea of applying the algorithm to only the differential components of the equation…
For the solution of discrete ill-posed problems, in this paper a novel preconditioned iterative method based on the Arnoldi algorithm for matrix functions is presented. The method is also extended to work in connection with Tikhonov…
We apply the iterative nonlinear programming method, previously proposed in our earlier work, to optimize Schur test functions and thereby provide refined upper bounds for the norms of integral operators. As an illustration, we derive such…
This paper provides a new approach to derive various arbitrary high order finite difference formulae for the numerical differentiation of analytic functions. In this approach, various first and second order formulae for the numerical…
We show the continuous dependence of solutions of linear nonautonomous second order parabolic partial differential equations (PDEs) with bounded delay on coefficients and delay. The assumptions are very weak: only convergence in the weak-*…