Symbolic analysis of bursting dynamical regimes of Rulkov neural networks

Time-Delay Identification Using Multiscale Ordinal Quantifiers

“…This hypothesis has been supported by recent studies of Bandt [27,28], Cuesta-Frau et al [29] and Gunther et al [30]. Actually, it has been previously shown that hierarchies and probabilities of the ordinal patterns offer a better characterization of the dynamical regimes of some complex systems, identifying transitions and behaviors that are not detected by more traditional statistical tools [31][32][33][34]. Ordinal patterns analysis can also be helpful to forecast extreme events in complex dynamics such as those obtained from an optically injected semiconductor laser [35], a semiconductor laser with optical feedback in the low frequency fluctuations regime [36], and a Raman fiber laser in the chaotic regime [37].…”

Control of coherence resonance in multiplex neural networks

“…We have found that a small percentage of randomly distributed inter-layer links can be sufficient to induce spikes in the "silent" layer. Further work will aim at using more advanced data analysis tools, such as symbolic ordinal analysis [37,38,39], to further characterize the regularity of the neuronal activity induced in layer 2.…”

Slow–Fast Dynamics Behaviors under the Comprehensive Effect of Rest Spike Bistability and Timescale Difference in a Filippov Slow–Fast Modified Chua’s Circuit Model

“…Figure 12a gives the coexistence response of the whole system when Ω = 0.027174, and the corresponding initial conditions from top to bottom are (x(0), y(0), z(0)) = (0, 0.5, 0.5), (x(0), y(0), z(0)) = (0, −0.5, −0.5) and (x(0), y(0), z(0)) = (−2, −2, 2.2), respectively. Numerical results show that there also exists a symmetrical period-1T E MTSOs (seen in Figure 12(a1)) besides the two coexisting asymmetrical period-1T E MBOs (seen in Figure 12(a2,a3)), indicating that tristability then exists in the whole system (3). Noting that the asymmetrical period-1T E MBOs in Figure 12(a3) is symmetrical with the one in Figure 11a, the corresponding generation mechanism can be obtained according to the symmetry.…”

“…With the assumption that Ω is small enough, i.e., 0 < Ω 1, then there exists an order gap between the rates of traditional variables (x, y and z) and the whole excitation, admitting that the system (3) may perform slow-fast dynamics behaviors. However, there is no apparent fast variables and slow variables in (3), indicating that the classical slow-fast decomposition method cannot be directly applied to (3) to explain the potential slow-fast dynamics behaviors such as bursting oscillations since the division of the slow subsystem and the fast subsystem in (3) is the first requirement for the application of this method. In order to apply the classical slow-fast decomposition method to deal with the potential slow-fast dynamics behaviors in (3), we now introduce the following rise-dimension method to realize the timescale separation in (3).…”

“…In the past decades, many research groups and scholars have studied slow-fast dynamical systems via experiments and computations based on extensive applications across many practical problems. For instance, neuronal activities and neural networks [1][2][3], calcium-ion oscillations in cells [4,5], catalytic oxidation reactions [6,7], and other applications [8][9][10].…”