Bitcore-p2p: Peer.connect does not work
I'm not sure what exactly you are trying to do with: 

peer.on('connected', function(){  console.log('connected'); });

You can just do on ready instead.

peer.on('ready', function(){  console.log('connected'); });

Example connecting to a peer and receiving notifications

var bitcore = require('bitcore-lib');
var Peer = require('bitcore-p2p').Peer;

var peer = new Peer({host: "101.201.31.79"});
//IP of one of the btc.com's miners

peer.on('ready', function(){
    console.log("Connected "+peer.version, peer.subversion, peer.bestHeight);
});
peer.on('disconnect', function(){
    console.log("disconnected");
});
//loop through peer notifications
peer.on('inv', function(message){
    var nodeMsg = message.inventory;
    var nodeMsgLen = nodeMsg.length;
    for (var i = 0; i &lt; nodeMsgLen; i++){
        console.log(nodeMsg[i].hash);
    };
});
//connect
peer.connect();