线上一个业务提供数据库使用功能，上线后记录了错误日志的功能，最近发现有万分之一的几率出现了这些mysql的错误，请问是如何出现的，该如何解决优化？

PHP版本：php5.1.0
MYSQL版本：5.1.57

[ 2015-08-12T08:50:36+08:00 ] ERR: SQLSTATE[HY000] [2013] Lost connection to MySQL server at 'reading final connect information', system error: 0 access ip:1.56.84.20
[ 2015-08-12T09:50:50+08:00 ] ERR: SQLSTATE[HY000] [2013] Lost connection to MySQL server at 'reading final connect information', system error: 0 access ip:123.116.122.63
[ 2015-08-12T10:50:23+08:00 ] ERR: SQLSTATE[HY000] [2013] Lost connection to MySQL server at 'reading authorization packet', system error: 0 access ip:222.161.250.114
[ 2015-08-12T11:51:45+08:00 ] ERR: SQLSTATE[HY000] [2013] Lost connection to MySQL server at 'reading final connect information', system error: 0 access ip:110.228.254.124
[ 2015-08-12T13:51:08+08:00 ] ERR: SQLSTATE[HY000] [2013] Lost connection to MySQL server at 'reading authorization packet', system error: 0 access ip:123.160.80.145
[ 2015-08-12T13:51:34+08:00 ] ERR: SQLSTATE[HY000] [2013] Lost connection to MySQL server at 'reading final connect information', system error: 0 access ip:58.252.49.21
[ 2015-08-12T15:11:03+08:00 ] ERR: SQLSTATE[HY000] [2013] Lost connection to MySQL server at 'reading authorization packet', system error: 0 access ip:182.124.51.229
[ 2015-08-12T04:14:54+08:00 ] ERR: SQLSTATE[08004] [1040] Too many connections access ip:218.93.161.197
[ 2015-08-12T04:15:09+08:00 ] ERR: SQLSTATE[08004] [1040] Too many connections access ip:106.57.122.118
[ 2015-08-12T04:15:17+08:00 ] ERR: SQLSTATE[08004] [1040] Too many connections access ip:183.226.252.253
[ 2015-08-12T04:15:34+08:00 ] ERR: SQLSTATE[08004] [1040] Too many connections access ip:106.39.252.137