Related papers: Explicit Construction of First Integrals by Singul…
In this paper, we consider a second order nonlinear ordinary differential equation of the form $\ddot{x}+k_1\frac{\dot{x}^2}{x}+(k_2+k_3x)\dot{x}+k_4x^3+k_5x^2+k_6x=0$, where $k_i$'s, $i=1,2,...,6,$ are arbitrary parameters. By using the…
Formal series solutions and the Kovalevskaya exponents of a quasi-homogeneous polynomial system of differential equations are studied by means of a weighted projective space and dynamical systems theory. A necessary and sufficient condition…
We present algorithms to solve coupled systems of linear differential equations, arising in the calculation of massive Feynman diagrams with local operator insertions at 3-loop order, which do {\it not} request special choices of bases.…
Dynamic systems characterized by second-order nonlinear ordinary differential equations appear in many fields of physics and engineering. To solve these kinds of problems, time-consuming step-by-step numerical integration methods and…
Continuous linear dynamical systems are used extensively in mathematics, computer science, physics, and engineering to model the evolution of a system over time. A central technique for certifying safety properties of such systems is by…
This paper discusses a new method to solve definite integrals using artificial neural networks. The objective is to build a neural network that would be a novel alternative to pre-established numerical methods and with the help of a…
Reachable set computation is an important technique for the verification of safety properties of dynamical systems. In this paper, we investigate reachable set computation for discrete nonlinear systems based on parallelotope bundles. The…
Discovering a suitable neural network architecture for modeling complex dynamical systems poses a formidable challenge, often involving extensive trial and error and navigation through a high-dimensional hyper-parameter space. In this…
A subalgebraic approximation algorithm is proposed to estimate from a set of time series the parameters of the observer representation of a discrete-time polynomial system without inputs which can generate an approximation of the observed…
Invariant manifolds are important constructs for the quantitative and qualitative understanding of nonlinear phenomena in dynamical systems. In nonlinear damped mechanical systems, for instance, spectral submanifolds have emerged as useful…
Generalized Linear Models are routinely used in data analysis. The classical procedures for estimation are based on Maximum Likelihood and it is well known that the presence of outliers can have a large impact on this estimator. Robust…
This paper introduces a novel method for the automatic detection and handling of nonlinearities in a generic transformation. A nonlinearity index that exploits second order Taylor expansions and polynomial bounding techniques is first…
Given a constant skew-symmetric matrix A, it is a difficult open problem whether the associated Lotka-Volterra system is integrable or not. We solve this problem in the special case when A is a Toepliz matrix where all off-diagonal entries…
In this research, the Bernoulli polynomials are introduced. The properties of these polynomials are employed to construct the operational matrices of integration together with the derivative and product. These properties are then utilized…
Our purpose in this paper is to study when a planar differential system polynomial in one variable linearizes in the sense that it has an inverse integrating factor which can be constructed by means of the solutions of linear differential…
We present a novel algorithm for generating robust and consistent hypotheses for multiple-structure model fitting. Most of the existing methods utilize random sampling which produce varying results especially when outlier ratio is high. For…
Accurate approximations of the change of system's output and its statistics with respect to the input are highly desired in computational dynamics. Ruelle's linear response theory provides breakthrough mathematical machinery for computing…
This paper focuses on the system identification of an important class of nonlinear systems: linearly parameterized nonlinear systems, which enjoys wide applications in robotics and other mechanical systems. We consider two system…
Real-time nonlinear Bayesian filtering algorithms are overwhelmed by data volume, velocity and increasing complexity of computational models. In this paper, we propose a novel ensemble based nonlinear Bayesian filtering approach which only…
We apply the results of singularity analysis to the isotropic cosmological models in general relativity and string theory with a variety of matter terms. For some of these models the standard Painlev\'{e} test is sufficient to demonstrate…