相关论文: Solvable Chaos
We report an infinite class of discrete hierarchies which naturally generalize familiar discrete KP one.
Undoing computations of a concurrent system is beneficial in many situations, e.g., in reversible debugging of multi-threaded programs and in recovery from errors due to optimistic execution in parallel discrete event simulation. A number…
In this paper, we study the fiber-chaos of switched linear dynamical systems.
Dynamical Systems theory generally deals with fixed point iterations of continuous functions. Computation by Turing machine although is a fixed point iteration but is not continuous. This specific category of fixed point iterations can only…
In this paper, we consider the problem of computing robust controlled invariants for discrete-time monotone dynamical systems. We consider different classes of monotone systems depending on whether the sets of states, control inputs and…
Dynamics of two anharmonic oscillators with interaction of the fourth order has been investigated. The conditions at realization of which system is integrable are established. The exact analytical solution of the nonlinear equations in the…
We demonstrate both theoretically and experimentally that the distribution of the wavefunction inside a partially open chaotic timereversal symmetric system displays significant deviations from the Porter Thomas distribution. We give…
Chaos is omnipresent in nature, and its understanding provides enormous social and economic benefits. However, the unpredictability of chaotic systems is a textbook concept due to their sensitivity to initial conditions, aperiodic behavior,…
Biological information processing is often carried out by complex networks of interconnected dynamical units. A basic question about such networks is that of reliability: if the same signal is presented many times with the network in…
We consider an elementary discrete process which starts from purely random configuration and leads to well-ordered and stable state. Complete analytical solution to this problem is presented.
Kinematical and dynamical properties of chaotic systems are reviewed and a few applications are described.
It is revealed that a special kind of Poisson stable point, which we call an unpredictable point, gives rise to the existence of chaos in the quasi-minimal set. The existing definitions of chaos are formulated in sets of motions. This is…
New integrable lattice systems are introduced, their different integrable discretization are obtained. B\"acklund transformations between these new systems and the relativistic Toda lattice (in the both continuous and discrete time…
In this paper, we deal with the classification complexity of continuous (Devaney) chaotic systems in dimensions $0,1$ and $\infty$ using the framework of invariant descriptive set theory. We identify the complexity in dimensions $0$ and…
We examine synchronization between identical chaotic systems. A rigorous criteria is presented which, if satisfied, guarantees that the coupling produces linearly stable synchronous motion. The criteria can also be used to design couplings…
We introduce a new class of "random" subsets of natural numbers, WM sets. This class contains normal sets (sets whose characteristic function is a normal binary sequence). We establish necessary and sufficient conditions for solvability of…
The wave properties of complex scattering systems that are large compared to the wavelength, and show chaos in the classical limit, are extremely sensitive to system details. A solution to the wave equation for a specific configuration can…
A systematic study of the discrete second order projective system is presented, complemented by the integrability analysis of the associated multilinear mapping. Moreover, we show how we can obtain third order integrable equations as the…
We consider two stable heteroclinic cycles rotating in opposite directions, coupled via diffusive terms. A complete synchronization in this system is impossible, and numerical exploration shows that chaos is abundant at low levels of…
The time needed to exchange information in the physical world induces a delay term when the respective system is modeled by differential equations. Time delays are hence ubiquitous, being furthermore likely to induce instabilities and with…