Related papers: Visualizing the logistic map with a microcontrolle…
We consider the problem of transporting \nota{one probability measure into another through} the flow of a given driftless control-affine system. Under suitable regularity conditions, the controllability of the system by means of open-loop…
Order-disorder transitions take place in many physical systems, but observing them in detail in real materials is difficult. In two- or quasi-two-dimensional systems, the transition has been studied by computer simulations and…
Motivated by a possibility to optimize modelling of the population evolution we postulate a generalization of the well-know logistic map. Generalized difference equation reads: \begin{equation} x_{n+1}=rx^p_n(1-x^q_n), \end{equation}…
In this article we consider the possibility of controlling the dynamics of nonlinear discrete systems. A new method of control is by mixing states of the system (or the functions of these states) calculated on previous steps. This approach…
Photonic circuits, engineered to couple optical modes according to a specific map, serve as processors for classical and quantum light. The number of components typically scales with that of processed modes, thus correlating system size,…
Labeled transition systems can be a great way to visualize the complex behavior of parallel and communicating systems. However, if, during a particular timeframe, no synchronization or communication between processes occurs, then multiple…
Bifurcation diagram is a powerful tool that visually gives information about the behavior of the equilibrium points of a dynamical system respect to the varying parameter. This paper proposes an educational algorithm by which the local…
Quasi-integrable Hamiltonian systems are of great interest in many research fields of physics and mathematics. In these systems, the phase space has regular and chaotic trajectories. These trajectories depend in part on the magnitude of…
We apply renormalized entropy as a complexity measure to the logistic and sine-circle maps. In the case of logistic map, renormalized entropy decreases (increases) until the accumulation point (after the accumulation point up to the most…
Nearly all nontrivial real-world systems are nonlinear dynamical systems. Chaos describes certain nonlinear dynamical systems that have a very sensitive dependence on initial conditions. Chaotic systems are always deterministic and may be…
We developed a powerful computational approach to elaborate on onset mechanisms of deterministic chaos due to complex homoclinic bifurcations in diverse systems. Its core is the reduction of phase space dynamics to symbolic binary…
The rapid increase in demand for wireless controlled Smart Lighting has created a need to automate the mapping between the identifiers for individual light sources and their physical locations. To control Smart Lights, their IDs and…
Modern space missions with uncrewed spacecraft require robust trajectory design to connect multiple chaotic orbits by small controls. To address this issue, we propose a control scheme to design robust trajectories by leveraging a…
The presence of physical systems whose characteristics change in a seemingly erratic manner gives rise to the study of chaotic systems. The characteristics of these systems are due to their hypersensitivity to changes in initial conditions.…
Delay-coordinate maps have been widely used recently to study nonlinear dynamical systems, where there is only access to the time series of one of their variables. Here, we show how the partial control method can be applied in this kind of…
A shift-periodic map is a one-dimensional map from the real line to itself which is periodic up to a linear translation and allowed to have singularities. It is shown that iterative sequences $x_{n+1}=F(x_n)$ generated by such maps display…
Offline map matching involves aligning historical trajectories of mobile objects, which may have positional errors, with digital maps. This is essential for applications in intelligent transportation systems (ITS), such as route analysis…
We consider a family of singular maps as an example of a simple model of dynamical systems exhibiting the property of robust chaos on a well defined range of parameters. Critical boundaries separating the region of robust chaos from the…
A scheme for logical computation using non-linear dynamical systems is presented. Examples of discrete-time maps configured as AND, OR, NAND and NOR gates are given. It is seen that the logical operations are flexible in the sense that an…
In this paper, an electronic circuit implementation of a robustly chaotic two-dimensional map is presented. Two such electronic circuits are realized. One of the circuits is configured as the driver and the other circuit is configured as…