in this paper by use of mathematical modeling of an observer [14,15] the notion of relative information functional for relative dynamical systemson compact metric spaces is presented. we extract the information function ofan ergodic dynamical system (x,t) from the relative information of t fromthe view point of observer χx, where x denotes the base space of the system.we also generalize the inv...

Epistemologically speaking, second language acquisition research (SLAR) might be reconsidered from a complex dynamical system view with interconnected aspects in the ecosystem of language acquisition. The present paper attempts to introduce the tenets of complex system theory and its application in SLAR. It has been suggested that the present dominant traditions in language acquisition research...

The concept of nonlinearity measures for dynamical systems is extended to estimation systems, which include both a dynamical model and a measurement model. For linear systems, propagation through linear dynamics and update by linear measurements both preserve the Gaussian property of a distribution of estimates. For nonlinear systems, how well a Gaussian distribution of estimates stays Gaussian...

In this paper we introduce the concept of entropy operator for continuous systems of finite topological entropy. It is shown that it generates the Kolmogorov entropy as a special case. If $phi$ is invertible then the entropy operator is bounded with the topological entropy of $phi$ as its norm.

Control systems with switching modes in which different dynamics are assigned are called hybrid dynamical systems and are being actively researched (1–6). The continuous behavior in the hybrid dynamical system is expressed generally by differential or difference equations, while the discrete behavior is described by logics or state machines such as automata. If a system can be regarded as a hyb...

In this paper, we present an example of control system design based on negative imaginary (NI) system theory. The system under consideration is an optical cavity system. A dynamical model of the cavity system is obtained through system identification of applied to experimental input output frequency response data obtained using a digital signal analyzer (DSA). The identified model satisfies NI ...

We numerically and theoretically investigate the behavior of a granular gas driven by asymmetric plates. The injection of energy in the dissipative system differs from one side to the opposite one. We prove that the dynamical clustering which is expected for such a system is affected by the asymmetry. As a consequence, the cluster position can be fully controlled. This property could lead to va...

We define a class 3 of topological dynamical systems, which are left invariant by coupled map lattice constructions. ‘fhis class .F has the property that if the coupling of the systems is sufficiently weak and (M, f) contains a hyperbolic set, ‘hen the new system $( M, f) obtained by the coupled map lattice construction has a hyperbolic set too. The coupled map attice construction, map 4, can b...

A nonlinear L2-gain property that generalizes the conventional (linear) notion of L2-gain for finite dimensional dynamical systems is studied. In particular, an optimizationbased approximation strategy that facilitates computation of gain bounds via a cascade is presented. The cascade in question consists of the dynamical system under test, driven by a nonlinear “energy saturation” operator tha...

We address the minimization of the sum of a proper, convex and lower semicontinuous with a (possibly nonconvex) smooth function from the perspective of an implicit dynamical system of forward-backward type. The latter is formulated by means of the gradient of the smooth function and of the proximal point operator of the nonsmooth one. The trajectory generated by the dynamical system is proved t...