AI 中文总结
该研究针对有限资源维持的Hindmarsh-Rose振子双层网络，通过度偏向马尔可夫过程分配资源，揭示拓扑偏向会重组同步暂态路径并产生非单调同步响应，证实混沌运动可在同步流形上保留。
AI 中文摘要
在由有限资源维持的振子网络中，同步性既取决于总资源量，也取决于资源的空间分布。我们研究一个双层系统：其活动层由混沌Hindmarsh-Rose振子构成，传输层则通过度偏向马尔可夫过程重新分配守恒资源。我们解析地表征了稳态资源场，确定了其存在性、唯一性及收敛性。通过将该场嵌入局部自适应反馈律，可将可用资源转换为节点相关的耗散，对此李雅普诺夫分析保证其收敛至同步流形。数值结果表明，拓扑偏向会重组同步的暂态路径：弱偏向产生几乎集体收缩，中等偏向形成由枢纽节点启动的招募层级，向中度节点和外围节点延伸；更强偏向下，度层级更显著，而外围节点的招募因自适应耗散集中于结构特权节点而放缓。在所探索的参数范围内，该定位-覆盖权衡伴随固定总资源下非单调的同步响应；同步后最大李雅普诺夫指数仍为正，关联维数仅小幅变化，这与横向偏差被抑制、同步流形上保留混沌运动一致。
英文摘要
In oscillator networks sustained by finite resources, synchronization can depend on both the total resource and its spatial distribution. We study a duplex system whose activity layer consists of chaotic Hindmarsh--Rose oscillators and whose transport layer redistributes a conserved resource through a degree-biased Markov process. The stationary resource field is characterized analytically, and its existence, uniqueness, and convergence are established. By embedding this field into a local adaptive feedback law, the available resource is converted into node-dependent dissipation, for which Lyapunov analysis guarantees convergence to the synchronization manifold. Numerical results show that topology bias reorganizes the transient route to synchronization. Weak bias produces an almost collective contraction, whereas intermediate bias creates a hub-initiated recruitment hierarchy that extends toward middle-degree and peripheral nodes. Under stronger bias, the degree hierarchy becomes more pronounced while peripheral recruitment slows because adaptive dissipation is concentrated on structurally privileged nodes. Across the explored parameter range, this localization--coverage tradeoff is accompanied by a non-monotonic synchronization response at fixed total resource. The largest Lyapunov exponent remains positive after synchronization and the correlation dimension changes only modestly, consistent with suppression of transverse deviations while chaotic motion is retained on the synchronization manifold.
