What are the neurological differences between varying types of love? It stands to reason that the biochemical cascade involved when a person experiences love, gives a feeling of well-being and drive.


  Studies in neuroscience have involved chemicals that are present in the brain and might be involved when people experience love. These chemicals include: nerve growth factor, testosterone, estrogen, dopamine, norepinephrine, serotonin, oxytocin, and vasopressin. Adequate brain levels of testosterone seem important for both human male and female sexual behavior. Dopamine, norepinephrine, and serotonin are more commonly found during the attraction phase of a relationship. Oxytocin and vasopressin seemed to be more closely linked to long term bonding and relationships characterized by strong attachments.


and


  Romantic and maternal love are highly rewarding
  experiences. Both are linked to the perpetuation of the species
  and therefore have a closely linked biological function of crucial
  evolutionary importance. 1


There's a lot of research about romantic love and parent/child love. Apparently there are correlations, between the neurological patterns observed with romantic and maternal love. 

I am wondering, do we know what the neurobiological differences are between romantic, maternal/paternal, platonic love and the  love of non-human entities for example a pet? 

1. The neurobiology of love
S. Zeki*
University College, Department of Anatomy, Gower Street, London WCIE 6BT, United Kingdom
It is very difficult to offer a response in the sense proposed, different researchers may have very different views. One of the keys in these research is to have clear differences between: attachment, attraction, sexual behavior, esthetics (philosophical theme), likes, interests, and very huge etc.

One can begin by reading Neil R. Carlson's chapter about reproductive behavior (Carlson, pp. 319-366) which addresses both hormonal and neural control of sexual behavior as well as maternal behavior from basic and general psychophysiological approaches.