Cron task with Elysia cron module run only manually?
As you said "the cron works only when I run it manually in the admin section (Elysia cron configuration), but I need it to be runing every some specific periode !", it tells your codes are working fine.

By default Drupal cron runs when site is accessed and it evaluates when was the last time cron ran, so if the prescribed time is passed cron will run again, but for that site needs to be accessed, so you have a task which is supposed to run at fix period, you can not wait for Drupal site to be accessed by some one, instead you need to set a crontab on your server which means your server will ping your cron.php at the scheduled time.

Check How to setup cron tab on Linux based system or as an alternate option you can use drush while setting up cron tab (see: cron.html).