Intermittent feedback induces attractor selection

A memory-based approach to model glorious uncertainties of love

We propose a minimal yet intriguing model for a relationship between two individuals. The feeling of an individual is modeled by a complex variable and, hence, has two degrees of freedom [Jafari et al., Nonlinear Dyn. 83, 615-622 (2016)]. The effect of memory of the other individual's behavior in the past has now been incorporated via a conjugate coupling between each other's feelings. A region of parameter space exhibits multi-stable solutions wherein trajectories with different initial conditions end up in different aperiodic trajectories. This aligns with the natural observation that most relationships are aperiodic and unique not only to themselves but, more importantly, to the initial conditions too. Thus, the inclusion of memory makes the task of predicting the trajectory of a relationship hopelessly impossible.

Space-dependent intermittent feedback can control birhythmicity

Birhythmicity is evident in many nonlinear systems, which include physical and biological systems. In some living systems, birhythmicity is necessary for response to the varying environment while unnecessary in some physical systems as it limits their efficiency. Therefore, its control is an important area of research. This paper proposes a space-dependent intermittent control scheme capable of controlling birhythmicity in various dynamical systems. We apply the proposed control scheme in five nonlinear systems from diverse branches of natural science and demonstrate that the scheme is efficient enough to control the birhythmic oscillations in all the systems. We derive the analytical condition for controlling birhythmicity by applying harmonic decomposition and energy balance methods in a birhythmic van der Pol oscillator. Further, the efficacy of the control scheme is investigated through numerical and bifurcation analyses in a wide parameter space. Since the proposed control scheme is general and efficient, it may be employed to control birhythmicity in several dynamical systems.

Impulsive feedback control of birhythmicity: Theory and experiment

We study the dynamic control of birhythmicity under an impulsive feedback control scheme where the feedback is made ON for a certain rather small period of time and for the rest of the time, it is kept OFF. We show that, depending on the height and width of the feedback pulse, the system can be brought to any of the desired limit cycles of the original birhythmic oscillation. We derive a rigorous analytical condition of controlling birhythmicity using the harmonic decomposition and energy balance methods. The efficacy of the control scheme is investigated through numerical analysis in the parameter space. We demonstrate the robustness of the control scheme in a birhythmic electronic circuit where the presence of noise and parameter fluctuations are inevitable. Finally, we demonstrate the applicability of the control scheme in controlling birhythmicity in diverse engineering and biochemical systems and processes, such as an energy harvesting system, a glycolysis process, and a p53-mdm2 network.

Resumption of dynamism in damaged networks of coupled oscillators

Deterioration in dynamical activities may come up naturally or due to environmental influences in a massive portion of biological and physical systems. Such dynamical degradation may have outright effect on the substantive network performance. This requires us to provide some proper prescriptions to overcome undesired circumstances. In this paper, we present a scheme based on external feedback that can efficiently revive dynamism in damaged networks of active and inactive oscillators and thus enhance the network survivability. Both numerical and analytical investigations are performed in order to verify our claim. We also provide a comparative study on the effectiveness of this mechanism for feedbacks to the inactive group or to the active group only. Most importantly, resurrection of dynamical activity is realized even in time-delayed damaged networks, which are considered to be less persistent against deterioration in the form of inactivity in the oscillators. Furthermore, prominence in our approach is substantiated by providing evidence of enhanced network persistence in complex network topologies taking small-world and scale-free architectures, which makes the proposed remedy quite general. Besides the study in the network of Stuart-Landau oscillators, affirmative influence of external feedback has been justified in the network of chaotic Rössler systems as well.