Explosive death in interacting networks under mixed coupling

Double explosive transitions in adaptive multilayer networks with higher-order interactions

Can asymmetry between two interacting networks fundamentally change how they synchronize? We identify double explosive transitions in the forward direction, backward direction, or a combination thereof, with single or double hysteresis loops in an adaptive bilayer multiplex network of Kuramoto oscillators with pairwise and three-body interactions and asymmetric phase lags. Using the Ott-Antonsen reduction, we derive a low-dimensional system and perform a stability analysis. The reduced model accurately captures the full microscopic dynamics and enables analytical expressions for the bifurcation points. Systematic mapping across multiple parameter planes reveals eight distinct synchronization regimes. The relative ordering of saddle-node and pitchfork bifurcation points---controlled by phase-lag asymmetry, cross-layer adaptation, and the higher-order interaction strength---creates two distinct coherent branches (weak and strong), giving rise to double explosive transitions. Crucially, phase-lag asymmetry acts as a robust control knob: while symmetric phase lags suppress explosive transitions, layer-specific differences promote multistability and double explosive transitions. The higher-order interaction strength $K_2$ and adaptation strengths $q$, $p$, and $h$ further modulate these transitions in a complex, parameter-dependent manner. Excellent agreement between analytical predictions and numerical simulations confirms the robustness of our reduced description.

Onset of explosive chimera death in coupled oscillators

Onset of synchronization in multiplex networks with higher order interactions

Control of network stochastic resonance in higher-order networks

The Kuramoto model is a canonical paradigm for characterizing the synchronization dynamics of coupled systems. Recently, Kuramoto systems with higher-order coupling have emerged as a growing research hotspot, yet most studies have largely focused on dynamical behavior analysis, with little attention on the control of global network behaviors. Building on the network stochastic resonance theory proposed by Wang et al (2026 Proc. R. Soc. A: Math. Phys. Eng. Sci. 482 20250945), this study extends the control channel from three-body coupling modulation to pairwise coupling modulation, and proposes an open-loop dynamical regulation strategy for global collective behaviors. This strategy leverages network stochastic resonance to achieve effective control without the need for real-time monitoring of the network. The findings of this research provide useful insights for the regulation of collective dynamics in higher-order coupled Kuramoto networks and the open-loop dynamic control of complex oscillator networks.

Suppression of explosive synchronization in adaptive Kuramoto oscillators with higher-order interactions

Adaptive higher-order interactions among coupled dynamical systems have found widespread applications in real-world systems. Such interactions are known to drive the system into an explosive first-order transition to synchronization. We employ a generalized adaptation function of the global order parameter to modulate the coupling strengths in a Kuramoto model with pairwise and triadic interactions, and to show that the adaptation exponents act as control parameters capable of suppressing explosive synchronization and reshaping the nature of the transition. We derive a self-consistency equation governing the dynamics of the system to determine the critical conditions for the onset of synchronization through the Ott-Antonsen ansatz. We find that positive adaptive exponents drive the system into an explosive first-order transition to synchronization, while negative exponents suppress it, steering the system toward a continuous second-order transition. All analytical predictions are validated through direct numerical simulations. Our results may be useful in understanding and controlling the nature of synchronization transitions in real-world systems where higher-order interactions and adaptive feedback coexist.

Emergent synchrony, metastability, and chaos in a mixed neuronal populations with higher-order interactions.

In this study, we investigate the emergent dynamics of mixed populations of self-oscillatory and excitable Izhikevich neurons embedded in a random network topology and interacting through both first-order and second-order interactions. By gradually increasing the strength of second-order interactions, we analyze its impact on synchronization, bursting dynamics, and metastability at the network level. Our results reveal a sequence of dynamical transitions from synchronized regular spiking to synchronized chaotic bursting, followed by a regime of fast chaotic spiking. The transition to chaotic bursting occurs via a spike adding route, while the subsequent transition to fast chaotic spiking is associated with the loss of the bifurcation structure responsible for burst termination, leading to the collapse of silent phases. We demonstrate that weak second-order interactions support complete cluster phase synchronization in both excitable and self-oscillatory neuronal populations, whereas increasing higher-order coupling induces a second-order transition to partially synchronized dynamics. This partially synchronized regime is characterized by synchronized bursting and metastability. Further increase in second-order interactions drives the network into a fully incoherent state characterized by irregular fast spiking. Additionally, we show that network link density strongly influences the degree of synchrony among self-oscillatory neurons but has limited impact on excitable neurons in the partial synchrony regime due to their heterogeneous firing rate distributions.