Feigenbaum scenario without parameters.

Typically, the period-doubling bifurcations exhibited by nonlinear dissipative systems are observed when varying systems' parameters. In contrast, the period-doubling bifurcations considered in the current research are induced by changing the initial conditions, whereas parameter values are fixed. Thus, the studied bifurcations can be classified as the period-doubling bifurcations without parameters. Moreover, we show a cascade of the period-doubling bifurcations without parameters, resulting in a transition to deterministic chaos. The explored effects are demonstrated by means of numerical modeling on an example of a modified Anishchenko-Astakhov self-oscillator where the ability to exhibit bifurcations without parameters is associated with the properties of a memristor. Finally, we compare the dynamics of the ideal-memristor-based oscillator with the behavior of a model taking into account the memristor forgetting effect.

Stochastic control of spiking activity bump expansion: Monotonic and resonant phenomena.

We consider spatially localized spiking activity patterns, so-called bumps, in ensembles of bistable spiking oscillators. The bistability consists in the coexistence of self-sustained spiking dynamics and a quiescent steady-state regime. We show numerically that the processes of growth or contraction of such patterns can be controlled by varying the intensity of multiplicative noise. In particular, the effect of noise is monotonic in an ensemble of coupled Hindmarsh-Rose oscillators. On the other hand, in another model proposed by Semenov et al. [Semenov et al., Phys. Rev. E 93, 052210 (2016)], a resonant noise effect is observed. In that model, stabilization of activity bump expansion is achieved at an appropriate noise level, and the noise effect reverses with a further increase in noise intensity. Moreover, we show the constructive role of nonlocal coupling that allows us to save domains and fronts being totally destroyed due to the action of noise in the case of local coupling.

Multiplexing-based control of stochastic resonance.

We show that multiplexing (Here, the term "multiplexing" means a special network topology where a one-layer network is connected to another one-layer networks through coupling between replica nodes. In the present paper, this term does not refer to the signal processing issues and telecommunications.) allows us to control noise-induced dynamics of multilayer networks in the regime of stochastic resonance. We illustrate this effect on an example of two- and multi-layer networks of bistable overdamped oscillators. In particular, we demonstrate that multiplexing suppresses the effect of stochastic resonance if the periodic forcing is present in only one layer. In contrast, multiplexing allows us to enhance the stochastic resonance if the periodic forcing and noise are present in all the interacting layers. In such a case, the impact of multiplexing has a resonant character: the most pronounced effect of stochastic resonance is achieved for an appropriate intermediate value of coupling strength between the layers. Moreover, multiplexing-induced enhancement of the stochastic resonance can become more pronounced for the increasing number of coupled layers. To visualize the revealed phenomena, we use the evolution of the dependence of the signal-to-noise ratio on the noise intensity for varying strength of coupling between the layers.

Subcritical Andronov-Hopf scenario for systems with a line of equilibria.

Using numerical simulation methods and analytical approaches, we demonstrate hard self-oscillation excitation in systems with infinitely many equilibrium points forming a line of equilibria in the phase space. The studied bifurcation phenomena are equivalent to the excitation scenario via the subcritical Andronov-Hopf bifurcation observed in classical self-oscillators with isolated equilibrium points. The hysteresis and bistability accompanying the discussed processes are shown and explained. The research is carried out on an example of a nonlinear memristor-based self-oscillator model. First, a simpler model including Chua's memristor with a piecewise-smooth characteristic is explored. Then, the memristor characteristic is changed to a function being smooth everywhere. Finally, the action of the memristor forgetting effect is taken into consideration.

Two-color optically addressed spatial light modulator as a generic spatiotemporal system.

Nonlinear spatiotemporal systems are the basis for countless physical phenomena in such diverse fields as ecology, optics, electronics, and neuroscience. The canonical approach to unify models originating from different fields is the normal form description, which determines the generic dynamical aspects and different bifurcation scenarios. Realizing different types of dynamical systems via one experimental platform that enables continuous transition between normal forms through tuning accessible system parameters is, therefore, highly relevant. Here, we show that a transmissive, optically addressed spatial light modulator under coherent optical illumination and optical feedback coupling allows tuning between pitchfork, transcritical, and saddle-node bifurcations of steady states. We demonstrate this by analytically deriving the system's dynamical equations in correspondence to the normal forms of the associated bifurcations and confirm these results via extensive numerical simulations. Our model describes a nematic liquid crystal device using nano-dimensional dichalcogenide (a-As 2S 3) glassy thin films as photo sensors and alignment layers, and we use device parameters obtained from experimental characterization. Optical coupling, for example, using diffraction, holography, or integrated unitary maps allows implementing a variety of system topologies of technological relevance for neural networks and potentially Ising or XY-Hamiltonian models with ultralow energy consumption.

Dissipative solitons for bistable delayed-feedback systems.

We study how nonlinear delayed-feedback in the Ikeda model can induce solitary impulses, i.e., dissipative solitons. The states are clearly identified in a virtual space-time representation of the equations with delay, and we find that conditions for their appearance are bistability of a nonlinear function and negative character of the delayed feedback. Both dark and bright solitons are identified in numerical simulations and physical electronic experiment, showing an excellent qualitative correspondence and proving thereby the robustness of the phenomenon. Along with single spiking solitons, a variety of compound soliton-based structures is obtained in a wide parameter region on the route from the regular dynamics (two quiescent states) to developed spatiotemporal chaos. The number of coexisting soliton-based states is fast growing with delay, which can open new perspectives in the context of information storage.

Andronov-Hopf bifurcation with and without parameter in a cubic memristor oscillator with a line of equilibria.

The model of a memristor-based oscillator with cubic nonlinearity is studied. The considered system has infinitely many equilibrium points, which build a line of equilibria in the phase space. Numerical modeling of the dynamics is combined with the bifurcational analysis. It has been shown that the oscillation excitation has distinctive features of the supercritical Andronov-Hopf bifurcation and can be achieved by changing of a parameter value as well as by variation of initial conditions. Therefore, the considered bifurcation is called Andronov-Hopf bifurcation with and without parameter.

Noise-induced transitions in a double-well excitable oscillator.

The model of a double-well oscillator with nonlinear dissipation is studied. The self-sustained oscillation regime and the excitable one are described. The first regime consists of the coexistence of two stable limit cycles in the phase space, which correspond to self-sustained oscillations of the point mass in either potential well. The self-sustained oscillations do not occur in a noise-free system in the excitable regime, but appropriate conditions for coherence resonance in either potential well can be achieved. The stochastic dynamics in both regimes is researched by using numerical simulation and electronic circuit implementation of the considered system. Multiple qualitative changes of the probability density function caused by noise intensity varying are explained by using the phase-space structure of the deterministic system.

Noise-induced transitions in a double-well oscillator with nonlinear dissipation.

We develop a model of bistable oscillator with nonlinear dissipation. Using a numerical simulation and an electronic circuit realization of this system we study its response to additive noise excitations. We show that depending on noise intensity the system undergoes multiple qualitative changes in the structure of its steady-state probability density function (PDF). In particular, the PDF exhibits two pitchfork bifurcations versus noise intensity, which we describe using an effective potential and corresponding normal form of the bifurcation. These stochastic effects are explained by the partition of the phase space by the nullclines of the deterministic oscillator.

Metal template assembly of highly functionalized octacyanoporphyrazine framework from TCNE structural units.

A new route to the octacyanoporphyrazine framework based on the interaction of metal sandwich pi-complexes with TCNE has been developed.