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[en] The mechanical and electrical properties, and information processing capabilities of microtubules are the permanent subject of interest for carrying out experiments in vitro and in silico, as well as for theoretical attempts to elucidate the underlying processes. In this paper, we developed a new model of the mechano–electrical waves elicited in the rows of very flexible C–terminal tails which decorate the outer surface of each microtubule. The fact that C–terminal tails play very diverse roles in many cellular functions, such as recruitment of motor proteins and microtubule–associated proteins, motivated us to consider their collective dynamics as the source of localized waves aimed for communication between microtubule and associated proteins. Our approach is based on the ferroelectric liquid crystal model and it leads to the effective asymmetric double-well potential which brings about the conditions for the appearance of kink–waves conducted by intrinsic electric fields embedded in microtubules. These kinks can serve as the signals for control and regulation of intracellular traffic along microtubules performed by processive motions of motor proteins, primarly from kinesin and dynein families. On the other hand, they can be precursors for initiation of dynamical instability of microtubules by recruiting the proper proteins responsible for the depolymerization process.
[en] The discrete Langevin-type equation, which can describe persistent processes, was introduced. The procedure of reconstruction of the equation from time series was proposed and tested on synthetic data, with short and long-tail distributions, generated by different Langevin equations. Corrections due to the finite sampling rates were derived. For an exemplary meteorological time series, an appropriate Langevin equation, which constitutes a stochastic macroscopic model of the phenomenon, was reconstructed.
[en] It is a common phenomenon that multi-scroll attractors are realized by introducing the various nonlinear functions with multiple breakpoints in double scroll chaotic systems. Differently, we present a nonautonomous approach for generating multi-double-scroll attractors (MDSA) without changing the original nonlinear functions. By using the multi-level-logic pulse excitation technique in double scroll chaotic systems, MDSA can be generated. A Chua's circuit, a Jerk circuit, and a modified Lorenz system are given as designed example and the Matlab simulation results are presented. Furthermore, the corresponding realization circuits are designed. The Pspice results are in agreement with numerical simulation results, which verify the availability and feasibility of this method.
[en] In the present paper, multi-degree-of-freedom strongly nonlinear systems are modeled as quasi-Hamiltonian systems and the stochastic averaging method for quasi-Hamiltonian systems (including quasi-non-integrable, completely integrable and non-resonant, completely integrable and resonant, partially integrable and non-resonant, and partially integrable and resonant Hamiltonian systems) driven by fractional Gaussian noise is introduced. The averaged fractional stochastic differential equations (SDEs) are derived. The simulation results for some examples show that the averaged SDEs can be used to predict the response of the original systems and the simulation time for the averaged SDEs is less than that for the original systems.
[en] The Kuramoto–Sakaguchi system of coupled phase oscillators, where interaction between oscillators is determined by a single harmonic of phase differences of pairs of oscillators, has very simple emergent dynamics in the case of identical oscillators that are globally coupled: there is a variational structure that means the only attractors are full synchrony (in-phase) or splay phase (rotating wave/full asynchrony) oscillations and the bifurcation between these states is highly degenerate. Here we show that nonpairwise coupling—including three and four-way interactions of the oscillator phases—that appears generically at the next order in normal-form based calculations can give rise to complex emergent dynamics in symmetric phase oscillator networks. In particular, we show that chaos can appear in the smallest possible dimension of four coupled phase oscillators for a range of parameter values.
[en] In this paper, a new memristor-based multi-scroll hyper-chaotic system is designed. The proposed memristor-based system possesses multiple complex dynamic behaviors compared with other chaotic systems. Various coexisting attractors and hidden coexisting attractors are observed in this system, which means extreme multistability arises. Besides, by adjusting parameters of the system, this chaotic system can perform single-scroll attractors, double-scroll attractors, and four-scroll attractors. Basic dynamic characteristics of the system are investigated, including equilibrium points and stability, bifurcation diagrams, Lyapunov exponents, and so on. In addition, the presented system is also realized by an analog circuit to confirm the correction of the numerical simulations.
[en] Motivated by the chaos suppression methods based on stabilizing an unstable periodic orbit, we study the stability of synchronized periodic orbits of coupled map systems when the period of the orbit is the same as the delay in the information transmission between coupled units. We show that the stability region of a synchronized periodic orbit is determined by the Floquet multiplier of the periodic orbit for the uncoupled map, the coupling constant, the smallest and the largest Laplacian eigenvalue of the adjacency matrix. We prove that the stabilization of an unstable τ-periodic orbit via coupling with delay τ is possible only when the Floquet multiplier of the orbit is negative and the connection structure is not bipartite. For a given coupling structure, it is possible to find the values of the coupling strength that stabilizes unstable periodic orbits. The most suitable connection topology for stabilization is found to be the all-to-all coupling. On the other hand, a negative coupling constant may lead to destabilization of τ-periodic orbits that are stable for the uncoupled map. We provide examples of coupled logistic maps demonstrating the stabilization and destabilization of synchronized τ-periodic orbits as well as chaos suppression via stabilization of a synchronized τ-periodic orbit.
[en] We study synchronization of systems in which agents holding chaotic oscillators move in a two-dimensional plane and interact with nearby ones forming a time dependent network. Due to the uncertainty in observing other agents' states, we assume that the interaction contains a certain amount of noise that turns out to be relevant for chaotic dynamics. We find that a synchronization transition takes place by changing a control parameter. But this transition depends on the relative dynamic scale of motion and interaction. When the topology change is slow, we observe an intermittent switching between laminar and burst states close to the transition due to small noise. This novel type of synchronization transition and intermittency can happen even when complete synchronization is linearly stable in the absence of noise. We show that the linear stability of the synchronized state is not a sufficient condition for its stability due to strong fluctuations of the transverse Lyapunov exponent associated with a slow network topology change. Since this effect can be observed within the linearized dynamics, we can expect such an effect in the temporal networks with noisy chaotic oscillators, irrespective of the details of the oscillator dynamics. When the topology change is fast, a linearized approximation describes well the dynamics towards synchrony. These results imply that the fluctuations of the finite-time transverse Lyapunov exponent should also be taken into account to estimate synchronization of the mobile contact networks.
[en] Spike-time correlations of neighbouring neurons depend on their intrinsic firing properties as well as on the inputs they share. Studies have shown that periodically firing neurons, when subjected to random shared input, exhibit asynchronicity. Here, we study the effect of random shared input on the synchronization of weakly coupled chaotic neurons. The cases of so-called electrical and chemical coupling are both considered, and we observe a wide range of synchronization behaviour. When subjected to identical shared random input, there is a decrease in the threshold coupling strength needed for chaotic neurons to synchronize in-phase. The system also supports lag–synchronous states, and for these, we find that shared input can cause desynchronization. We carry out a master stability function analysis for a network of such neurons and show agreement with the numerical simulations. The contrasting role of shared random input for complete and lag synchronized neurons is useful in understanding spike-time correlations observed in many areas of the brain.
[en] We study the dynamics of coupled phase oscillators on a two-dimensional Kuramoto lattice with periodic boundary conditions. For coupling strengths just below the transition to global phase-locking, we find localized spatiotemporal patterns that we call “frequency spirals.” These patterns cannot be seen under time averaging; they become visible only when we examine the spatial variation of the oscillators' instantaneous frequencies, where they manifest themselves as two-armed rotating spirals. In the more familiar phase representation, they appear as wobbly periodic patterns surrounding a phase vortex. Unlike the stationary phase vortices seen in magnetic spin systems, or the rotating spiral waves seen in reaction-diffusion systems, frequency spirals librate: the phases of the oscillators surrounding the central vortex move forward and then backward, executing a periodic motion with zero winding number. We construct the simplest frequency spiral and characterize its properties using analytical and numerical methods. Simulations show that frequency spirals in large lattices behave much like this simple prototype.