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.

Pathway selection by an active droplet.

We report the movement of an active 1-pentanol drop within a closed Y-shaped channel subjected to geometrical and chemical asymmetry. A Y-shaped channel was configured with an angle of 120° between any two arms, which serves as the closed area of movement for the active drop. The arm where the 1-pentanol drop is introduced in the beginning is considered the source arm, and the center of the Y-shaped structure is the decision region. The drop always selects a specific route to move away from the decision region. The total probability of pathway selection excludes the possibility of the drop choosing the source channel. Remarkably, the active drop exhibits a strong sense of navigation for both geometrically and chemically asymmetric environments with accuracy rates of 80% and 100%, respectively. The pathway selection in a chemically asymmetric channel is a demonstration of the artificial negative chemotaxis, where the extra confined drop acts as a chemo-repellent. To develop a better understanding of our observations, a numerical model is constructed, wherein the particle is subjected to a net force which is a combined form of - (i) Yukawa-like repulsive interaction force (acting between the drop and the walls), (ii) a self-propulsion force, (iii) a drag, and (iv) a stochastic force. The numerics can capture all the experimental findings both qualitatively and quantitatively. Finally, a statistical analysis validates conclusions derived from both experiments and numerics.

Regulating dynamics through intermittent interactions.

In this article we experimentally demonstrate an efficient scheme to regulate the behavior of coupled nonlinear oscillators through dynamic control of their interaction. It is observed that introducing intermittency in the interaction term as a function of time or the system state predictably alters the dynamics of the constituent oscillators. Choosing the nature of the interaction, attractive or repulsive, allows for either suppression of oscillations or stimulation of activity. Two parameters Δ and τ, that reign the extent of interaction among subsystems, are introduced. They serve as a harness to access the entire range of possible behaviors from fixed points to chaos. For fixed values of system parameters and coupling strength, changing Δ and τ offers fine control over the dynamics of coupled subsystems. We show this experimentally using coupled Chua's circuits and elucidate their behavior for a range of coupling parameters through detailed numerical simulations.

Emergent rhythms in coupled nonlinear oscillators due to dynamic interactions.

The role of a new form of dynamic interaction is explored in a network of generic identical oscillators. The proposed design of dynamic coupling facilitates the onset of a plethora of asymptotic states including synchronous states, amplitude death states, oscillation death states, a mixed state (complete synchronized cluster and small amplitude desynchronized domain), and bistable states (coexistence of two attractors). The dynamical transitions from the oscillatory to the death state are characterized using an average temporal interaction approximation, which agrees with the numerical results in temporal interaction. A first-order phase transition behavior may change into a second-order transition in spatial dynamic interaction solely depending on the choice of initial conditions in the bistable regime. However, this possible abrupt first-order like transition is completely non-existent in the case of temporal dynamic interaction. Besides the study on periodic Stuart-Landau systems, we present results for the paradigmatic chaotic model of Rössler oscillators and the MacArthur ecological model.

Aging in global networks with competing attractive-Repulsive interaction.

We study the dynamical inactivity of the global network of identical oscillators in the presence of mixed attractive and repulsive coupling. We consider that the oscillators are a priori in all to all attractive coupling and then upon increasing the number of oscillators interacting via repulsive interaction, the whole network attains a steady state at a critical fraction of repulsive nodes, pc. The macroscopic inactivity of the network is found to follow a typical aging transition due to competition between attractive-repulsive interactions. The analytical expression connecting the coupling strength and pc is deduced and corroborated with numerical outcomes. We also study the influence of asymmetry in the attractive-repulsive interaction, which leads to symmetry breaking. We detect chimera-like and mixed states for a certain ratio of coupling strengths. We have verified sequential and random modes to choose the repulsive nodes and found that the results are in agreement. The paradigmatic networks with diverse dynamics, viz., limit cycle (Stuart-Landau), chaos (Rössler), and bursting (Hindmarsh-Rose neuron), are analyzed.

Static and dynamic attractive-repulsive interactions in two coupled nonlinear oscillators.

Many systems exhibit both attractive and repulsive types of interactions, which may be dynamic or static. A detailed understanding of the dynamical properties of a system under the influence of dynamically switching attractive or repulsive interactions is of practical significance. However, it can also be effectively modeled with two coexisting competing interactions. In this work, we investigate the effect of time-varying attractive-repulsive interactions as well as the hybrid model of coexisting attractive-repulsive interactions in two coupled nonlinear oscillators. The dynamics of two coupled nonlinear oscillators, specifically limit cycles as well as chaotic oscillators, are studied in detail for various dynamical transitions for both cases. Here, we show that dynamic or static attractive-repulsive interactions can induce an important transition from the oscillatory to steady state in identical nonlinear oscillators due to competitive effects. The analytical condition for the stable steady state in dynamic interactions at the low switching time period and static coexisting interactions are calculated using linear stability analysis, which is found to be in good agreement with the numerical results. In the case of a high switching time period, oscillations are revived for higher interaction strength.