In this paper, we study the limit behavior of trajectories of a nonlinear and discontinuous model of opinion dynamics based on the notion of bounded confidence. This model was previously studied in the case where the influence function has the form i(v) = v. It was shown that, under a particular condition on parameters of the system, any its trajectory tends to a fixed point. In this paper, we prove a similar result under weaker conditions on the influence function: it is assumed that i(v) is continuous, nonstrictly increasing, and i(v) = 0 if and only if v = 0.

中文翻译：

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一种观点动力学模型中的定点收敛

在本文中，我们基于有界置信度概念研究了非线性且不连续的意见动力学模型的轨迹的极限行为。先前曾在影响函数的形式为i（v）= v的情况下研究过此模型。结果表明，在特定的系统参数条件下，其任何轨迹都趋于固定点。在本文中，我们证明了在较弱条件下的影响函数的相似结果：假设i（v）是连续的，非严格增加的，并且当且仅当v = 0时i（v）= 0。