The structural balance preserving problem is studied in this article for heterogeneous agents in the state-dependent cooperation-competition network. The heterogeneous agents considered are described by second-order integrator systems with different intrinsic nonlinear dynamics, and velocity damping terms, and the initial network is structurally balanced, and connected, which can be divided into two cooperation subnetworks. To solve this problem, a novel classification strategy is applied, where two kinds of evolution rules among agents, and the distributed protocol based on a class of potential functions are proposed, respectively. Under this strategy, the heterogeneous multi-agent system can not only maintain the structural balance of cooperation-competition networks but also achieve bipartite static consensus. Finally, a numerical example is delivered to demonstrate the effectiveness of the theoretical analysis.

中文翻译：

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合作竞争网络中异构代理的结构平衡保持和两方静态共识

针对状态依赖合作竞争网络中的异构主体，研究了结构平衡保持问题。所考虑的异构主体由具有不同固有非线性动力学和速度阻尼项的二阶积分器系统描述，并且初始网络在结构上是平衡的并相互连接，可以分为两个协作子网络。为了解决这个问题，提出了一种新颖的分类策略，提出了两种代理之间的演化规则，并提出了基于一类潜在函数的分布式协议。在这种策略下，异构的多主体系统不仅可以维持合作竞争网络的结构平衡，而且可以实现两方静态共识。最后，