Chimeric states induced by higher-order interactions in coupled prey-predator systems.

Higher-order interactions have been instrumental in characterizing the intricate complex dynamics in a diverse range of large-scale complex systems. Our study investigates the effect of attractive and repulsive higher-order interactions in globally and non-locally coupled prey-predator Rosenzweig-MacArthur systems. Such interactions lead to the emergence of complex spatiotemporal chimeric states, which are otherwise unobserved in the model system with only pairwise interactions. Our model system exhibits a second-order transition from a chimera-like state (mixture of oscillating and steady state nodes) to a chimera-death state through a supercritical Hopf bifurcation. The origin of these states is discussed in detail along with the effect of the higher-order non-local topology which leads to the rise of a distinct and dynamical state termed as "amplitude-mediated chimera-like states." Our study observes that the introduction of higher-order attractive and repulsive interactions exhibit incoherence and promote persistence in consumer-resource population dynamics as opposed to susceptibility shown by synchronized dynamics with only pairwise interactions, and these results may be of interest to conservationists and theoretical ecologists studying the effect of competing interactions in ecological networks.

First-order transition to oscillation death in coupled oscillators with higher-order interactions.

We investigate the dynamical evolution of Stuart-Landau oscillators globally coupled through conjugate or dissimilar variables on simplicial complexes. We report a first-order explosive phase transition from an oscillatory state to oscillation death, with higher-order (2-simplex triadic) interactions, as opposed to the second-order transition with only pairwise (1-simplex) interactions. Moreover, the system displays four distinct homogeneous steady states in the presence of triadic interactions, in contrast to the two homogeneous steady states observed with dyadic interactions. We calculate the backward transition point analytically, confirming the numerical results and providing the origin of the dynamical states in the transition region. The results are robust against the application of noise. The study will be useful in understanding complex systems, such as ecological and epidemiological, having higher-order interactions and coupling through conjugate variables.

Solitary death in coupled limit cycle oscillators with higher-order interactions.

Coupled limit cycle oscillators with pairwise interactions are known to depict phase transitions from an oscillatory state to amplitude or oscillation death. This Research Letter introduces a scheme to incorporate higher-order interactions which cannot be decomposed into pairwise interactions and investigates the dynamical evolution of Stuart-Landau oscillators under the impression of such a coupling. We discover an oscillator death state through a first-order (explosive) phase transition in which a single, coupling-dependent stable death state away from the origin exists in isolation without being accompanied by any other stable state usually existing for pairwise couplings. We call such a state a solitary death state. Contrary to widespread subcritical Hopf bifurcation, here we report homoclinic bifurcation as an origin of the explosive death state. Moreover, this explosive transition to the death state is preceded by a surge in amplitude and followed by a revival of the oscillations. The analytical value of the critical coupling strength for the solitary death state agrees with the simulation results. Finally, we point out the resemblance of the results with different dynamical states associated with epileptic seizures.

Advent of extreme events in predator populations.

We study the dynamics of a ring of patches with vegetation-prey-predator populations, coupled through interactions of the Lotka-Volterra type. We find that the system yields aperiodic, recurrent and rare explosive bursts of predator density in a few isolated spatial patches from time to time. Further, the global predator biomass also exhibits sudden uncorrelated occurrences of large deviations from the mean as the coupled system evolves. The maximum value of the predator population in a patch, as well as the maximum value of the predator biomass, increases with coupling strength. These trends are further corroborated by fits to Generalized Extreme Value distributions, where the location and scale factor of the distribution increases markedly with coupling strength, indicating the crucial role of coupling interactions in the generation of extreme events. These results indicate how occurrences of extremely large predator populations can emerge in coupled population dynamics, and in a more general context they suggest a generic class of deterministic nonlinear systems that can naturally exhibit extreme events.

Amplitude chimera and chimera death induced by external agents in two-layer networks.

We report the emergence of stable amplitude chimeras and chimera death in a two-layer network where one layer has an ensemble of identical nonlinear oscillators interacting directly through local coupling and indirectly through dynamic agents that form the second layer. The nonlocality in the interaction among the dynamic agents in the second layer induces different types of chimera-related dynamical states in the first layer. The amplitude chimeras developed in them are found to be extremely stable, while chimera death states are prevalent for increased coupling strengths. The results presented are for a system of coupled Stuart-Landau oscillators and can, in general, represent systems with short-range interactions coupled to another set of systems with long-range interactions. In this case, by tuning the range of interactions among the oscillators or the coupling strength between two types of systems, we can control the nature of chimera states and the system can also be restored to homogeneous steady states. The dynamic agents interacting nonlocally with long-range interactions can be considered as a dynamic environment or a medium interacting with the system. We indicate how the second layer can act as a reinforcement mechanism on the first layer under various possible interactions for desirable effects.

Explosive death in nonlinear oscillators coupled by quorum sensing.

Many biological and chemical systems exhibit collective behavior in response to the change in their population density. These elements or cells communicate with each other via dynamical agents or signaling molecules. In this work, we explore the dynamics of nonlinear oscillators, specifically Stuart-Landau oscillators and Rayleigh oscillators, interacting globally through dynamical agents in the surrounding environment modeled as a quorum sensing interaction. The system exhibits the typical continuous second-order transition from oscillatory state to death state, when the oscillation amplitude is small. However, interestingly, when the amplitude of oscillations is large we find that the system shows an abrupt transition from oscillatory to death state, a transition termed "explosive death." So the quorum-sensing form of interaction can induce the usual second-order transition, as well as sudden first-order transitions. Further, in the case of the explosive death transitions, the oscillatory state and the death state coexist over a range of coupling strengths near the transition point. This emergent regime of hysteresis widens with increasing strength of the mean-field feedback, and is relevant to hysteresis that is widely observed in biological, chemical, and physical processes.

Explosive death in complex network.

We report the emergence of an explosive death transition in a network of identical oscillators interacting to other oscillators through nonlocal coupling in the presence of a common environment. This transition has an abrupt and irreversible characteristic in parameter space which has been a common signature of first order phase transition. For the similar coupling scheme, both ensemble of chaotic and periodic oscillators showed qualitatively similar kind of transition, hence making it a universal transition. The details of which along with dependence of environmental and nonlocal coupling on this first-order like phase transition is also discussed.

Explosive death induced by mean-field diffusion in identical oscillators.

We report the occurrence of an explosive death transition for the first time in an ensemble of identical limit cycle and chaotic oscillators coupled via mean-field diffusion. In both systems, the variation of the normalized amplitude with the coupling strength exhibits an abrupt and irreversible transition to death state from an oscillatory state and this first order phase transition to death state is independent of the size of the system. This transition is quite general and has been found in all the coupled systems where in-phase oscillations co-exist with a coupling dependent homogeneous steady state. The backward transition point for this phase transition has been calculated using linear stability analysis which is in complete agreement with the numerics.

Phase-flip and oscillation-quenching-state transitions through environmental diffusive coupling.

We study the dynamics of nonlinear oscillators coupled through environmental diffusive coupling. The interaction between the dynamical systems is maintained through its agents which, in turn, interact globally with each other in the common dynamical environment. We show that this form of coupling scheme can induce an important transition like phase-flip transition as well transitions among oscillation quenching states in identical limit-cycle oscillators. This behavior is analyzed in the parameter plane by analytical and numerical studies of specific cases of the Stuart-Landau oscillator and van der Pol oscillator. Experimental evidences of the phase-flip transition and quenching states are shown using an electronic version of the van der Pol oscillators.