Fig 11 - uploaded by Suresh Ramachandran
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Circuit block diagram of the three coupled time delayed feedback oscillator for the subsystem coupling configuration ((18)-(20)).
Source publication
We investigate and report an experimental confirmation of zero-lag synchronization (ZLS) in a system of three coupled time-delayed piecewise linear electronic circuits via dynamical relaying with different coupling configurations, namely mutual and subsystem coupling configurations. We have observed that when there is a feedback between the central...
Contexts in source publication
Context 1
... we consider the coupling configuration, where the relay system sends its delayed signal to the two outer systems and only one system (here system 2) sends its delayed feedback to the relay system. This configuration is called a subsystem coupling. The circuit for the subsystem coupling configuration is shown in Fig. 11 as a block diagram. The state equations for the coupled electronic circuit (Fig. 11) can be written as follows: (a) Time evolution of both the outer circuits (U 2(t) -yellow curve and U3(t) -blue curve) displaying ZLS; x-axis: 1 unit −2 ms, y-axis: 1 unit −2 V and (b) time series of the relay and one of the outer circuits showing IPS ...
Context 2
... relay system sends its delayed signal to the two outer systems and only one system (here system 2) sends its delayed feedback to the relay system. This configuration is called a subsystem coupling. The circuit for the subsystem coupling configuration is shown in Fig. 11 as a block diagram. The state equations for the coupled electronic circuit (Fig. 11) can be written as follows: (a) Time evolution of both the outer circuits (U 2(t) -yellow curve and U3(t) -blue curve) displaying ZLS; x-axis: 1 unit −2 ms, y-axis: 1 unit −2 V and (b) time series of the relay and one of the outer circuits showing IPS (yellow curve U 1(t) and blue curve U2(t)). x-axis: 1 unit −2 ms, y-axis: 1 unit −2 V. ...
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Citations
... The synchronization of complex dynamical networks means that all the nodes in a complex networks eventually approaches to trajectory of a target 52 The European Physical Journal Special Topics node. Currently, there are many types of concepts of synchronization, such as complete synchronization [4,5], lag synchronization [6], zero-lag synchronization [7], generalized synchronization [8], anti-synchronization [9], projective synchronization [10], quasi-synchronization [11] and breathing synchronization [12]. In practical cases, time delay appears in the electronic applications of dynamical systems. ...
This paper investigates the problem of projective lag synchronization behavior in drive-response dynamical networks (DRDNs) with identical and non-identical nodes. An adaptive control method is designed to achieve projective lag synchronization with fully unknown parameters and unknown bounded disturbances. These parameters were estimated by adaptive laws obtained by Lyapunov stability theory. Furthermore, sufficient conditions for synchronization are derived analytically using the Lyapunov stability theory and adaptive control. In addition, the unknown bounded disturbances are also overcome by the proposed control. Finally, analytical results show that the states of the dynamical network with non-delayed coupling can be asymptotically synchronized onto a desired scaling factor under the designed controller. Simulation results show the effectiveness of the proposed method.
... The bifurcation scenario and the dynamics of this time delayed chaotic oscillator has been investigated in some detail in Refs. [15], [17]. The nonlinear function can be effectively implemented by a piecewise linear function defined as ...
We study the synchronization dynamics of mutually time-delay coupled intrinsic time-delay systems. In particular, we analyze the phase synchronized states and phase-flip transitions occurring in a bi-directionally time-delay coupled electronic circuit model with threshold nonlinearity using both numerical simulations and direct experiment. By varying the coupling delay for different coupling strengths, we identify the changes in the relative phase between the oscillators from in-phase to anti-phase and vice versa. We also carry out a detailed analysis by solving the delay differential equations numerically to confirm the phase-flip transition. Finally, the numerical predictions are verified with experiments.
... For the TPWL system we choose the form of the nonlinear function as given by [Suresh et al., 2013] ...
We point out the existence of transition from partial to global generalized
synchronization (GS) in symmetrically coupled regular networks (array, ring,
global and star) of distinctly different time-delay systems of different orders
using the auxiliary system approach and the mutual false nearest neighbor
method. It is established that there exists a common GS manifold even in an
ensemble of structurlly nonidentical time-delay systems with different fractal
dimensions and we find that GS occurs simultaneously with phase synchronization
(PS) in these networks. We calculate the maximal transverse Lyapunov exponent
to evaluate the asymptotic stability of the complete synchronization manifold
of each of the main and the corresponding auxiliary systems, which, in turn,
ensures the stability of the GS manifold between the main systems. Further, we
also estimate the correlation coefficient and the correlation of probability of
recurrence to establish the relation between GS and PS. We also deduce an
analytical stability condition for partial and global GS using the
Krasovskii-Lyapunov theory.
This work investigates the dynamical behaviors of the third-order chaotic oscillator with threshold controller as its nonlinear element. The system reveals several complex dynamics with the presence and absence of external excitation. For a specific set of control parameter values, the system exhibits three different routes, which include the regular period-doubling route, period-3 doubling to chaos, and three tori to chaos are realized with the aid of bifurcation and Lyapunov exponents. In particular, by tuning the values of the parameters, the coexistence of multiple attractors is also revealed. More interestingly, we uncovered strange nonchaotic attractors (SNA) in a single periodically forced system through an intermittency route. The presence of SNA behaviors is calculated by using several characterizing quantities such as Lyapunov exponent, Poincarè section, singular-continuous spectrum analysis, and 0–1 test analysis. The performance of the system is investigated using the fixed-point analysis, numerical integration of mathematical model, and real-time experimental results.
We point out the existence of a transition from partial to global generalized synchronization (GS) in symmetrically coupled structurally different time-delay systems of different orders using the auxiliary system approach and the mutual false nearest neighbor method. The present authors have recently reported that there exists a common GS manifold even in an ensemble of structurally nonidentical scalar time-delay systems with different fractal dimensions and shown that GS occurs simultaneously with phase synchronization (PS). In this paper we confirm that the above result is not confined just to scalar one-dimensional time-delay systems alone but there exists a similar type of transition even in the case of time-delay systems with different orders. We calculate the maximal transverse Lyapunov exponent to evaluate the asymptotic stability of the complete synchronization manifold of each of the main and the corresponding auxiliary systems, which in turn ensures the stability of the GS manifold between the main systems. Further we estimate the correlation coefficient and the correlation of probability of recurrence to establish the relation between GS and PS. We also calculate the mutual false nearest neighbor parameter which doubly confirms the occurrence of the global GS manifold.
Zero-lag synchronization between distant cortical areas has been observed in a diversity of experimental data sets and between many different regions of the brain. Several computational mechanisms have been proposed to account for such isochronous synchronization in the presence of long conduction delays: Of these, the phenomenon of “dynamical relaying” – a mechanism that relies on a specific network motif – has proven to be the most robust with respect to parameter mismatch and system noise. Surprisingly, despite a contrary belief in the community, the common driving motif is an unreliable means of establishing zero-lag synchrony. Although dynamical relaying has been validated in empirical and computational studies, the deeper dynamical mechanisms and comparison to dynamics on other motifs is lacking. By systematically comparing synchronization on a variety of small motifs, we establish that the presence of a single reciprocally connected pair – a “resonance pair” – plays a crucial role in disambiguating those motifs that foster zero-lag synchrony in the presence of conduction delays (such as dynamical relaying) from those that do not (such as the common driving triad). Remarkably, minor structural changes to the common driving motif that incorporate a reciprocal pair recover robust zero-lag synchrony. The findings are observed in computational models of spiking neurons, populations of spiking neurons and neural mass models, and arise whether the oscillatory systems are periodic, chaotic, noise-free or driven by stochastic inputs. The influence of the resonance pair is also robust to parameter mismatch and asymmetrical time delays amongst the elements of the motif. We call this manner of facilitating zero-lag synchrony resonance-induced synchronization, outline the conditions for its occurrence, and propose that it may be a general mechanism to promote zero-lag synchrony in the brain.
The present paper explores the synchronization scenario of hyperchaotic time-delayed electronic oscillators coupled indirectly via a common environment. We show that depending upon the coupling parameters a hyperchaotic time-delayed system can show in-phase or complete synchronization, and also inverse-phase or anti-synchronization. This paper reports the {\it first} experimental confirmation of synchronization of hyperchaos in time-delayed electronic oscillators coupled indirectly through a common environment. We confirm the occurrence of in-phase and inverse-phase synchronization phenomena in the coupled system through the dynamical measures like generalized autocorrelation function, correlation of probability of recurrence, and the concept of localized sets computed directly from the experimental time-series data. We also present a linear stability analysis of the coupled system to predict the onset of synchronization in parameter space. The experimental and analytical results are further supported by the detailed numerical analysis of the coupled system. Apart from the above mentioned measures, we numerically compute another quantitative measure, namely, Lyapunov exponent spectrum of the coupled system that confirms the transition from the in-phase (inverse-phase) synchronized state to the complete (anti-) synchronized state with the increasing coupling strength.
Zero-lag synchronization between distant cortical areas has been observed in
a diversity of experimental data sets and between many different regions of the
brain. Several computational mechanisms have been proposed to account for such
isochronous synchronization in the presence of long conduction delays: Of
these, the phenomena of "dynamical relaying" - a mechanism that relies on a
specific network motif (M9) - has proven to be the most robust with respect to
parameter and system noise. Surprisingly, despite a contrary belief in the
community, the common driving motif (M3) is an unreliable means of establishing
zero-lag synchrony. Although dynamical relaying has been validated in empirical
and computational studies, the deeper dynamical mechanisms and comparison to
dynamics on other motifs is lacking. By systematically comparing
synchronization on a variety of small motifs, we establish that the presence of
a single reciprocally connected pair - a "resonance pair" - plays a crucial
role in disambiguating those motifs that foster zero-lag synchrony in the
presence of conduction delays (such as dynamical relaying, M9) from those that
do not (such as the common driving triad, M3). Remarkably, minor structural
changes to M3 that incorporate a reciprocal pair (hence M6, M9, M3+1) recover
robust zero-lag synchrony. The findings are observed in computational models of
spiking neurons, populations of spiking neurons and neural mass models, and
arise whether the oscillatory systems are periodic, chaotic, noise-free or
driven by stochastic inputs. The influence of the resonance pair is also robust
to parameter mismatch and asymmetrical time delays amongst the elements of the
motif. We call this manner of facilitating zero-lag synchrony resonance-induced
synchronization and propose that it may be a general mechanism to promote
zero-lag synchrony in the brain.
