Related papers: Synthesizing the L\"{u} attractor by parameter-swi…
We prove, by employing rigorous numerics, that Shimizu-Morioka system has a Lorenz attractor for an open set of parameter values. Using this result, we prove the existence of a discrete version of the Lorenz attractor for a class of…
Introduced as a model for hyperchaos, the generalized R"ossler system of dimension N is obtained by linearly coupling N-3 additional degrees of freedom to the original R"ossler equation. Under variation of a single control parameter, it is…
When analyzing probabilistic computations, a powerful approach is to first find a martingale---an expression on the program variables whose expectation remains invariant---and then apply the optional stopping theorem in order to infer…
We take a new approach to construct Quintessential models. With this approach, we first easily obtain a tracker solution that is different from those discovered before and straightforwardly find a solution of multiple attractors, i.e., a…
We study the synthesis problem for distributed architectures with a parametric number of finite-state components. Parameterized specifications arise naturally in a synthesis setting, but thus far it was unclear how to detect realizability…
In this paper we present methods for the synthesis of polynomial invariants for probabilistic transition systems. Our approach is based on martingale theory. We construct invariants in the form of polynomials over program variables, which…
Pursuing our work in [18], [17], [20], [5], we consider in this article the two-dimensional thermohydraulics equations. We discretize these equations in time using the implicit Euler scheme and we prove that the global attractors generated…
Reactive synthesis is a technology for the automatic construction of reactive systems from logical specifications. In these lecture notes, we study different algorithms for the reactive synthesis problem of linear-time temporal logic (LTL).…
In this paper we propose a novel semi-definite programming based method to compute robust domains of attraction for state-constrained perturbed polynomial systems. A robust domain of attraction is a set of states such that every trajectory…
We study LTLf synthesis with multiple properties, where satisfying all properties may be impossible. Instead of enumerating subsets of properties, we compute in one fixed-point computation the relation between product-game states and the…
This article describes a method for constructing approximations to periodic solutions of dynamic Lorenz system with classical values of the system parameters. The author obtained a system of nonlinear algebraic equations in general form…
An attractor of a piecewise-smooth continuous system of differential equations can bifurcate from a stable equilibrium to a more complicated invariant set when it collides with a switching manifold under parameter variation. Here numerical…
We consider the problem of asymptotic reconstruction of the state and parameter values in systems of ordinary differential equations. A solution to this problem is proposed for a class of systems of which the unknowns are allowed to be…
We describe a framework for bounding extreme values of quantities on global attractors of differential dynamical systems. A global attractor is the minimal set that attracts all bounded sets; it contains all forward-time limit points. Our…
We provide a method to identify system parameters of dynamical systems, called ID-ODE -- Inference by Differentiation and Observing Delay Embeddings. In this setting, we are given a dataset of trajectories from a dynamical system with…
In this paper, the Parameter Switching (PS) algorithm is used to approximate numerically attractors of a Hopfield Neural Network (HNN) system. The PS algorithm is a convergent scheme designed for approximating attractors of an autonomous…
We show that a common language can be used to unify the description of parametrically-coupled circuits--parametric amplifiers, frequency converters, and parametric nonreciprocal devices--with that of band-pass filter and impedance matching…
Synthesizer is a type of electronic musical instrument that is now widely used in modern music production and sound design. Each parameters configuration of a synthesizer produces a unique timbre and can be viewed as a unique instrument.…
This study introduces a modified quadratic Lorenz attractor. The properties of this new chaotic system are analysed and discussed in detail, by determining the equilibria points, the eigenvalues of the Jacobian, and the Lyapunov exponents.…
Reactive synthesis is a key technique for the design of correct-by-construction systems and has been thoroughly investigated in the last decades. It consists in the synthesis of a controller that reacts to environment's inputs satisfying a…