AIX

hello,
A process allowed the maximum number of network connections in the AIX system?

So I think you're asking how many network connections a process is allowed to have in AIX. The limit is more about file descriptors. Check the output of ulimit -a. On an AIX 7.1 system I use I get

core file size              (blocks, -c) 2097151
data seg size               (kbytes, -d) 262144
file size                   (blocks, -f) unlimited
max memory size             (kbytes, -m) unlimited
open files                          (-n) 4000
pipe size                (512 bytes, -p) 64
stack size                  (kbytes, -s) 32768
cpu time                   (seconds, -t) unlimited
max user processes                  (-u) unlimited
virtual memory              (kbytes, -v) unlimited

You care about the "open files" limit. You can change this limit using ulimit -n <number>, e.g. ulimit -n 8000 or ulimit -n unlimited. Read the man page for ulimit on other ways to change the limits permanently or across multiple users.