What happens in a small scale blockchain network?
If you were using a fork of Bitcoin Core, your small scale network would not work.

Assuming you did the basic chain parameter modification or just firewall yourself from the rest of the Bitcoin network, there are two major things that are missing: peer discover, and mining.

Bitcoin Core by default uses a process called DNS Seeding in order to discover seed nodes. If those seeders fail, it will fall back to using some hard coded seed nodes. However, these are seed nodes which are treated differently than normal nodes (even though they are still normal nodes). Seed nodes are only connected to in order to get a list of more nodes to connect to. It is nodes on that list that are eventually connected to for actual normal node operations. Your node disconnects from those seed nodes once they get this list.

So, for your network, you would need to potentially run your own DNS seeders and seed nodes. But that's actually not really necessary. You would just need to disable DNS seeding and the hardcoded seed nodes, then just have everyone on your network set multiple connect=&lt;ip&gt; lines in their configuration files where &lt;ip&gt; is the IP address of a node. This will force the node to connect only to the specified nodes. Note that this will disable further node discovery and automatic node connection, so if you add someone else to your network, not all of the other nodes will connect to the newcomer unless they are explicitly added.

The other problem will be mining. Bitcoin Core does not contain any mining logic at all. It does not automatically mine nor does it even have the ability to produce blocks. Instead you will need to install some other mining software. However, because CPU and GPU mining are pointless, you will have to build, and potentially modify, those mining software yourself in order to enable CPU and GPU mining. Otherwise you will need to get some mining hardware supported by those software. Without using any mining software, your network will not produce any blocks and no transactions will be confirmed.