Bifurcation delay in a network of locally coupled slow-fast systems

Imperfect chimera and synchronization in a hybrid adaptive conductance based exponential integrate and fire neuron model

In this study, the hybrid conductance-based adaptive exponential integrate and fire (CadEx) neuron model is proposed to determine the effect of magnetic flux on conductance-based neurons. To begin with, bifurcation analysis is carried out in relation to the input current, resetting parameter, and adaptation time constant in order to comprehend dynamical transitions. We exemplify that the existence of period-1, period-2, and period-4 cycles depends on the magnitude of input current via period doubling and period halving bifurcations. Furthermore, the presence of chaotic behavior is discovered by varying the adaptation time constant via the period doubling route. Following that, we examine the network behavior of CadEx neurons and discover the presence of a variety of dynamical behaviors such as desynchronization, traveling chimera, traveling wave, imperfect chimera, and synchronization. The appearance of synchronization is especially noticeable when the magnitude of the magnetic flux coefficient or the strength of coupling strength is increased. As a result, achieving synchronization in CadEx is essential for neuron activity, which can aid in the realization of such behavior during many cognitive processes.

Additional complex conjugate feedback-induced explosive death and multistabilities

Many natural and man-made systems require suitable feedback to function properly. In this study, we aim to investigate the impact of additional complex conjugate feedback on globally coupled Stuart-Landau oscillators. We find that this additional feedback results in the onset of symmetry breaking clusters and out-of-phase clusters. Interestingly, we also find the existence of explosive amplitude death along with disparate multistable states. We characterize the first-order transition to explosive death through the amplitude order parameter and show that the transition from oscillatory to death state indeed shows a hysteresis nature. Further, we map the global dynamical transitions in the parametric spaces. In addition, to understand the existence of multistabilities and their transitions, we analyze the bifurcation scenarios of the reduced model and also explore their basin stability. Our study will shed light on the emergent dynamics in the presence of additional feedback.

A nonlinear memductance induced intermittent and anti-phase synchronization

We introduce a model to mimic the dynamics of oscillators that are coupled by mean-field nonlinear memductance. Notably, nonlinear memductance produces dynamic nonlinearity, which causes the direction of coupling to change over time. Depending on the parameters, such a dynamic coupling drives the trajectory of oscillators to a synchronization or anti-synchronization manifold. Specifically, depending on the forcing frequency and coupling strength, we find anti-phase and intermittent synchronization. With the increase in coupling magnitude, one can observe a transition from intermittent synchronization to complete synchronization through anti-phase synchronization. The results are validated through numerical simulations. The hypothesis has a huge impact on the study of neuronal networks.

Effect of processing delay on bifurcation delay in a network of slow-fast oscillators

Bifurcation delay or slow passage effect occurs in dynamical systems with slow-fast time-varying parameters. In this work, we report the impact of processing delay on bifurcation delay in a network of locally coupled slow-fast systems with self-feedback delay. We report that the network exhibits coexisting coherent (synchronized) and incoherent (desynchronized) states among the oscillators as a function of various parameters like self-feedback delay, processing delay, and amplitude of the external current. In particular, we show the decrease of the synchronized region (control of synchronization) for (i) a fixed value of processing delay with varying self-feedback delay and (ii) fixed self-feedback delay with increasing processing delay. In contrast, we observe the increase of the synchronized region (control of desynchronization) for fixed processing delay and self-feedback delay while varying the amplitude of the external current. Finally, we have also analyzed the effect of processing delay on bifurcation delay with the presence of noise and we report that the inhomogeneity in the additional noise does not affect the asymmetry in a bifurcation delay.