The Inverse Frobenius-Perron problem (IFPP) concerns the creation of discrete chaotic mappings with arbitrary invariant densities. In this note, we present a new and elegant solution to the IFPP, based on positive matrix theory. Our method allows chaotic maps with arbitrary piecewise-constant invariant densities, and with arbitrary mixing properties, to be synthesized.

I review the local theory of mixing, which focuses on infinitesimal blobs of scalar being advected and stretched by a random velocity field. An advantage of this theory is that it provides elegant analytical results. A disadvantage is that it is highly idealised. Nevertheless, it provides insight into the mechanism of chaotic mixing and the effect of random fluctuations on the rate of decay of ...

The extent of chaos and the suppressory role of Coulomb repulsion in the chaotic dynamics associated with nonsteady finite-amplitude electroconvection is revisited in the context of dynamical systems. Specifically, it is theoretically demonstrated that the threshold value of the charge density taming the heteroclinic chaos associated with laminar chaotic mixing depends on the sinusoidal perturb...

The game of Plinko, as seen on the CBS television show The Price Is Right, demonstrates rich chaotic dynamics as evidenced by a strong sensitivity to initial conditions. This behavior can be readily observed by watching repeated runs of the Plinko puck and noting the final location of the puck once it has passed through the peg lattice: despite the fact that many runs often start nearly co-loca...

An adaptive projection-based reduced-order model (ROM) formulation is presented for model-order reduction of problems featuring chaotic and convection-dominant physics. efficient method formulated to adapt the basis at every time-step on-line execution account unresolved dynamics. The ROM in a Least-Squares setting using variable transformation promote stability robustness. strategy developed i...

A number of approaches to the design of communications systems with chaos have recently been proposed [Kocarev et al., 1992; Belsky & Dmitriev, 1993; Cuomo et al., 1993; Dedieu et al., 1993; Halle et al., 1993; Volkovskii & Rul’kov, 1993]. Low-frequency physical experiments demonstrating a principle possibility of such system realization have also been made [Kocarev et al., 1992; Bohme et al., ...

Amongst possible choices for identifying complicated processes for prediction, simulation, and approximation applications, high-order Takagi-Sugeno (TS) fuzzy models are fitting tools. Although they can construct models with rather high complexity, they are not as interpretable as first-order TS fuzzy models. In this paper, we first propose to use Deformed Linear Models (DLMs) in consequence pa...

The problem of dynamic adaptation prediction algorithms in chaotic environments based on identification the situations-analogs database retrospective observations is considered. Under conditions symmetrical and unsymmetrical dynamics, traditional computational schemes precedent turn out to be ineffective. In this regard, a analysis method evolutionary modeling proposed. Implementation scheme fo...

‎in this paper‎, ‎we have investigated the chaotic behavior of thermal convection in couple stress liquid saturated porous layer subject to gravity‎, ‎heated from below and cooled from above‎, ‎based on theory of dynamical system‎. ‎a low dimensional lorenz‎- ‎like model is obtained by using galerkin-truncation approximation‎. ‎we found that there is proportional relation between scaled couple ...