Search results for "Multistability"
showing 9 items of 19 documents
Hidden attractors in dynamical systems
2016
Complex dynamical systems, ranging from the climate, ecosystems to financial markets and engineering applications typically have many coexisting attractors. This property of the system is called multistability. The final state, i.e., the attractor on which the multistable system evolves strongly depends on the initial conditions. Additionally, such systems are very sensitive towards noise and system parameters so a sudden shift to a contrasting regime may occur. To understand the dynamics of these systems one has to identify all possible attractors and their basins of attraction. Recently, it has been shown that multistability is connected with the occurrence of unpredictable attractors whi…
Polymorphic and regular localized activity structures in a two-dimensional two-component reaction–diffusion lattice with complex threshold excitation
2010
Abstract Space–time dynamics of the system modeling collective behaviour of electrically coupled nonlinear units is investigated. The dynamics of a local cell is described by the FitzHugh–Nagumo system with complex threshold excitation. It is shown that such a system supports formation of two distinct kinds of stable two-dimensional spatially localized moving structures without any external stabilizing actions. These are regular and polymorphic structures. The regular structures preserve their shape and velocity under propagation while the shape and velocity as well as other integral characteristics of polymorphic structures show rather complex temporal behaviour. Both kinds of structures r…
Four-phase patterns in a forced nonlinear optical oscillator
2009
We present preliminary theoretical and experimental results indicating that a high Fresnel number nonlinear optical oscillator with planar mirrors can display four-phase multistability, eventually leading to four-phase patterns. Such situation is similar to that emerging in extended oscillatory systems forced within a 4:1 resonance and, to the best of our knowledge, has not been predicted nor observed previously in an optical system.
Optomechanical systems close to the conservative limit
2017
In dissipative optomechanical systems, the total damping hits negative values at the parametric instability point. This also corresponds to the phonon lasing threshold, where the mechanical resonator enters in the self-induced oscillations regime. This paper shows that the two mentioned phenomena are delayed from each other when the optomechanical systems operate close to their conservative limit, where the mechanical damping is very small. In fact, the total damping can be negative and very small for a while before the phonon lasing happens. As a result, the linearized theory is extended over the negative damping region where the mechanical displacements remain very small. It follows that …
Correlation effects in bistability at the nanoscale: Steady state and beyond
2012
The possibility of finding multistability in the density and current of an interacting nanoscale junction coupled to semi-infinite leads is studied at various levels of approximation. The system is driven out of equilibrium by an external bias and the nonequilibrium properties are determined by real-time propagation using both time-dependent density functional theory (TDDFT) and many-body perturbation theory (MBPT). In TDDFT the exchange-correlation effects are described within a recently proposed adiabatic local density approximation (ALDA). In MBPT the electron-electron interaction is incorporated in a many-body self-energy which is then approximated at the Hartree-Fock (HF), second-Born,…
Hidden attractors in dynamical models of phase-locked loop circuits : limitations of simulation in MATLAB and SPICE
2017
During recent years it has been shown that hidden oscillations, whose basin of attraction does not overlap with small neighborhoods of equilibria, may significantly complicate simulation of dynamical models, lead to unreliable results and wrong conclusions, and cause serious damage in drilling systems, aircrafts control systems, electromechanical systems, and other applications. This article provides a survey of various phase-locked loop based circuits (used in satellite navigation systems, optical, and digital communication), where such difficulties take place in MATLAB and SPICE. Considered examples can be used for testing other phase-locked loop based circuits and simulation tools, and m…
Competing Phases Involving Spin-State and Ligand Structural Orderings in a Multistable Two-Dimensional Spin Crossover Coordination Polymer
2017
[EN] Competition between spin-crossover and structural ligand ordering is identified as responsible for multistability and generation of six different phases in a rigid two-dimensional coordination polymer formulated {Fe-II[Hg-II(SCN)(3)](2) mu-(4,4'-bipy)(2)}(n) (1) (4,4'-bipy = 4,4'-bipyridine). The structure of 1 consists of infinite linear [Fe(mu-4,4'-bipy)](n)(2n+) chains linked by in situ formed {[Hg-II(SCN)(3)](2)(mu-4,4'-bipy)}(2n-) anionic dimers. The thermal dependence of the high-spin fraction, his, features four magnetic phases defined by steps following the sequence gamma(HS) = 1 (phase 1) gamma(HS) = 1/2 (phase 2) gamma(HS) approximate to 1/3 (phase 3) gamma(HS) = 0 (phase 4) …
Effect of N-substitution in multinuclear complexes allows interplay between magnetic states and multistability investigated by Mössbauer spectroscopy
2006
A series of pentadentate ligands N-X-5LH2 (X=H, Methyl, Benzyl)=N-X-saldptn (4-X-N,N′-bis(l-hydroxy-2-benzylidene)-1,7-diamino-4-azaheptane) has been prepared by a Schiff base condensation between 1,7-diamino-4-X-azaheptane and salicylaldehyde. Complexation with Fe(III) yields a series of high-spin (S=5/2) complexes of [FeIII(N-X-5L)Cl]. Such precursors were combined with [Mo(CN)8]4− and a series of blue nonanuclear cluster compounds [MoIV(CN)FeIII(N-X-5L)8]Cl4 resulted. Such star-shaped nonanuclear compounds are high-spin systems at room temperature. On cooling to 10K some of the iron(III) centers switched to the low-spin state as proven by Mossbauer spectra, i.e. multiple electronic trans…
Coexistence of hidden attractors and multistability in counterexamples to the Kalman conjecture
2019
The Aizerman and Kalman conjectures played an important role in the theory of global stability for control systems and set two directions for its further development – the search and formulation of sufficient stability conditions, as well as the construction of counterexamples for these conjectures. From the computational perspective the latter problem is nontrivial, since the oscillations in counterexamples are hidden, i.e. their basin of attraction does not intersect with a small neighborhood of an equilibrium. Numerical calculation of initial data of such oscillations for their visualization is a challenging problem. Up to now all known counterexamples to the Kalman conjecture were const…