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This paper introduces the \textit{truncator} map as a dynamical system on the space of configurations of an interacting particle system. We represent the symbolic dynamics generated by this system as a non-commutative algebra and classify…
The model system manifesting phenomena peculiar to complex analytic maps is offered. The system is a non-autonomous ring cavity with nonlinear elements and filters,
Dynamic Occupancy Grid Mapping is a technique used to generate a local map of the environment containing both static and dynamic information. Typically, these maps are primarily generated using lidar measurements. However, with improvements…
We investigate numerically and experimentally dynamical systems having three interacting frequencies: a discrete mapping (a circle map), an exactly solvable model (a system of coupled ordinary differential equations), and an experimental…
We present a method to detect the unstable periodic orbits of a multidimensional chaotic dynamical system. Our approach allows us to locate in an efficient way the unstable cycles of, in principle, arbitrary length with a high accuracy.…
Iterations of odd piecewise continuous maps with two discontinuities, i.e., symmetric discontinuous bimodal maps, are studied. Symbolic dynamics is introduced. The tools of kneading theory are used to study the homology of the discrete…
A procedure to characterize chaotic dynamical systems with concepts of complex networks is pursued, in which a dynamical system is mapped onto a network. The nodes represent the regions of space visited by the system, while edges represent…
Dynamical phase transitions are defined as non-analytic points of the large deviation function of current fluctuations. We show that for boundary driven systems, many dynamical phase transitions can be identified using the geometrical…
Dynamical systems theory has long provided a foundation for understanding evolving phenomena across scientific domains. Yet, the application of this theory to complex real-world systems remains challenging due to issues in mathematical…
Dynamical systems are a broad class of mathematical tools used to describe the evolution of physical and computational processes. Traditionally these processes model changing entities in a static world. Picture a ball rolling on an empty…
It is demonstrated that very general nonlinear dynamical systems covering all cases arising in practice can be brought down to rate equations of chemical kinetics
In this paper we consider sufficient conditions for the existence of uniform compact global attractor for non-autonomous dynamical systems in special classes of infinite-dimensional phase spaces. The obtained generalizations allow us to…
Standandard Hamiltonian mechanics in its homogeneous formulation is applied to the study of discontinuities representing rapid changes of Hamiltonians. Different formulations of Hamiltonian mechanics are reviewed. An original representation…
For finite-dimensional quantum systems, such as qubits, a well established strategy to protect such systems from decoherence is dynamical decoupling. However many promising quantum devices, such as oscillators, are infinite dimensional, for…
The concept of random dynamical system is a comparatively recent development combining ideas and methods from the well developed areas of probability theory and dynamical systems. Due to our inaccurate knowledge of the particular physical…
Invariant manifolds provide the geometric structures for describing and understanding dynamics of nonlinear systems. The theory of invariant manifolds for both finite and infinite dimensional autonomous deterministic systems, and for…
Modelling interactions is critical in learning complex dynamical systems, namely systems of interacting objects with highly non-linear and time-dependent behaviour. A large class of such systems can be formalized as $\textit{geometric…
We consider the dynamics of a droplet on a vibrating fluid bath. This hydrodynamic quantum analog system is shown to elicit the canonical behavior of damped-driven systems, including a period doubling route to chaos. By approximating the…
Some of the basic properties of any dynamical system can be summarized by a graph. The dynamical systems in our theory run from maps like the logistic map to ordinary differential equations to dissipative partial differential equations. Our…
We generalize a method of control of chaos which uses delayed feedback at the period of an unstable orbit to stabilize that orbit. The generalization consists of substituting some portion of the nonlinear dynamical system with a delayed…