lyaponuv function —— Model thinking lecture note (6)

本文探讨了李雅普诺夫函数在模型中作为稳定性的关键角色,通过两个假设阐述其如何确保系统达到平衡状态。文章还讨论了市场交换作为李雅普诺夫过程的一个实例,以及该函数可能引导系统进入局部最优而非全局最优的问题。

摘要生成于 C知道 ,由 DeepSeek-R1 满血版支持, 前往体验 >

If we can set up a lyaponuv function for the model, then this system means it can go to equilibrium. 

F(x) is a lyaponuv function.

Assumption1: F(x) has a maximum value.

Assumption2:if x(t+1) != x(t) F(x(t+1)) > F(x(t)) + K where K > 0

claim: At some point x(t+1) = x(t)

The time it takes to converge in equalibrium = (maximum state - minimum state) / periodic transistion number;

lyaponuv may come to local optima which means the system will not stay in the maximum or minimum state.

Exchange market is an good example of lyaponuv function process.(without negative externities which means nothing will prevent the increment or decrement)

lyaponuv process end up in stochastic equilibrium comparing to the unique equilibrium in marckov process

评论
添加红包

请填写红包祝福语或标题

红包个数最小为10个

红包金额最低5元

当前余额3.43前往充值 >
需支付:10.00
成就一亿技术人!
领取后你会自动成为博主和红包主的粉丝 规则
hope_wisdom
发出的红包
实付
使用余额支付
点击重新获取
扫码支付
钱包余额 0

抵扣说明:

1.余额是钱包充值的虚拟货币,按照1:1的比例进行支付金额的抵扣。
2.余额无法直接购买下载,可以购买VIP、付费专栏及课程。

余额充值