First of all as you have mentioned in comment section ,I am here with providing the references of Concept of HariHara present in Puranas.
Let's first look at Harivamsa purana - Vishnu Parva -Chapter 125 - Fighting stops between Rudra and Krishna and Hymn to Harihara . This whole chapter is dedicated to the concept of HariHara and there is a Stotra (Hymn) by Sage Markandeya called "HariHaratmaka Stotra" in this chapter.
And here isSanskrit-Hindi version.
Below are some verses.
शिवाय विष्णुरूपाय विष्णवे शिवरूपिणे ।
यथान्तरं न पश्यामि तेन तौ
shivAya viShNurUpAya viShNave shivarUpiNe |
pashyAmi tena tau dishataH shivam ||125-29 ||
I do not see any difference between shiva in the form of viShNu and
viShNu in the form of shiva. They provide auspiciousness to the world.
तदेव ते प्रवक्ष्यामि रूपं
tadeva te pravakShyAmi
rUpaM hariharAtmakam ||125-30||
I proclaim that the form with the soul of hari (viShNu) and hara
(shiva) has no beginning, middle and end (destruction). This form is
imperishable and having no decline.
विष्णुर्विष्णोश्च परम: शिव:।
एक एव द्विधाभूतो लोके चरति
rudrasya paramo viShNurviShNoshcha paramaH shivaH |
eka eva dvidhA
bhUto loke charati nityashaH ||125-41 ||
The supreme lord of rudra (shiva) is viShNu and the supreme lord of
viShNu is shiva (rudra). The same lord is moving in the world always
in two forms.
न विना शंकर विष्णुर्न विना केशवं शिव: ।
तस्मादेकत्वमायातौ रुद्रोपेन्द्रौ तु तौ पुरा ।||42||
na vinA sha~NkaraM viShNurna vinA keshavaM shivaH |
tasmAdekatvamAyAtau rudropendrau tu tau purA |
viShNu does not exist without sha~Nkara (shiva) and shiva does not
exist without keshava (viShNu). Hence, rudra (shiva) and upendra
(kR^iShNa - viShNu) have attained oneness, since long before.
At which time was this concept developed?
So as we can see from above verses that the concept of Harihara is an ancient concept and it's roots also can be traced back to Mahabharata itself.
अजेयस्त्वं त्रिभिरर्लोर्के: सदेवासुरमानुषे :|
शिवाय विष्णुरुपाय विष्णवेशिवरुपिणे || 76 ||
MB Book 3 - Vana Parva -Kairata parva -SECTION XXXIX - Verse 76
P.89 Thou art Siva in the form of Vishnu, and Vishnu in the form of
The concept was also there at the time of Adi Shankaracharya i.e early 8th century as mentioned in Shankara Digvijayam
The Acharya continued his travels and visited holy places like
Gokarna, Hari-Shankara (present-day Harihar where he sang eleven
verses in praise of the combined form of Shiva and Vishnu), as well as
Mookambika, the temple of great spiritual power where he stayed for
several days adoring the Devi.
And from his own work called Vivekachudamani or Crest-jewel of discrimination.
नारायणोऽहं नरकान्तकोऽहं पुरान्तकोऽहं पुरुषोऽहमीशः ।
अखण्डबोधोऽहमशेषसाक्षी निरीश्वरोऽहं निरहं च निर्ममः ॥ 494 ॥
nārāyaṇo'haṃ narakāntako'haṃ purāntako'haṃ puruṣo'hamīśaḥ |
akhaṇḍabodho'hamaśeṣasākṣī nirīśvaro'haṃ nirahaṃ ca nirmamaḥ || 494 ||
- I am Nārāyaṇa, the slayer of Nāraka; I am the destroyer of Tripura, the Supreme Being, the Ruler; I am knowledge Absolute, the
Witness of everything; I have no other Ruler but myself, I am devoid
of the ideas of "I’ and "mine".
What is the precise meaning of the Harihara concept?
The precise meaning of the Harihara concept can be described by looking at the verses from scriptures
so the basic concept was already there in vedic literature as a base like " All that exists is Brahman" " - sarvam khalvidam brahma " - 'सर्वं खल्विदं ब्रह्म'. This concept is basically a unification of two different aspects or powers of same supreme lord into one , which are having two different purposes to achieve.
Rudra is Vishnu and Vishnu is Rudra .The one supreme lord is dwelling in both .
There is no Vishnu without Shiva and no Shiva without Vishnu. And these two are one since the beginning . There is no difference in between these two. Just like water mixed with water becomes water itself , these two gods combined becomes one supreme lord . Brahman ब्रह्मन. and this is not so precise but somewhat close meaning of Harihara.
Which theological problem should be solved by this concept?
The HariHara concept has tried to bridge the gap and philosophical differences between devotees of these two sects , as well as others. This is one of the solution of theological problem offered by the concept.
Apart from that the concept also served a purpose of clearing the doubts from the minds of people ,and made them aware of one supreme truth ,which is basic concept of hinduism scriptures by eliminating duality or difference in the forms of the Supreme God.
So this concept kept alive the spirit of Vedas and the Vedantas. And established devotional harmony among followers of Vedic path or we can say Hinduism.
Scholarly articles - :
Preceptors of Advaita - Chapter 60 - THE SAGE OF KANCHI by T. M. P. Mahadevan M.A., PH.D. is quoting the views of His Holiness Sri Chandrasekhara Saraswati,Sri Sankarachrya of Kanchi Kamakoti Pitha.
On another occasion speaking on the same theme, the Āchārya observed:
“Because two people worship different manifestations of One Supreme
Being, there is no warrant for their quarrelling with each other. The
Śiva-purāṇas extol Śiva and the Viṣṇu-purāṇas extol Viṣṇu. But a
proper understanding will remove the misconception. The praise of a
particular manifestation in a Purāṇa is to be understood in its
context and not as absolute. How can there be a higher or lower,
superior or inferior when in reality there are not two, but it is only
One God manifesting differently? We must not forget that there are
works which proclaim the oneness of Śiva and Viṣṇu, of Hara and Hari.
It has been declared that the enemies of Śiva are the enemies of Viṣṇu
too, and vice versa.
The following is a brief account of the significance and gist of the
Āchārya’s teachings:— A major division in Hinduism is that between
Vaiṣṇavism and Śaivism. The Āchārya is never tired of pointing out
that, according to all our Scriptures and the teachings of all the
great masters, Śiva and Viṣṇu are one. Our ancients have taught us in
several ways the unity of Godhead. The conceptions of Naṭarāja and
Rangarāja are complementary to each other. In fact, Brahmā, Viṣṇu and
Śiva are but different aspects of the same Deity. A similar
complementariness is to be noticed in the idea of God as male and
female, as father and mother. The integrated views of the Deity as
Harihara , and as Ardhanārīśvara , have a deep significance, and take
us nearer the supreme truth.
Here this is Advaita article about concept of HariHara or Siva-viShNu-abheda
And finally is an article portion related HarHara non difference - Lord Siva and His Worship -Siva and Vishnu are One. Sri Swami Sivananda
By - A DIVINE LIFE SOCIETY PUBLICATION