The following shlokas from Srimad Bhagavatam glorify the four plenary expansions of Lord Narayana.
The four expansions of Lord Narayana are
• Vasudeva
• Sankarshana
• Pradhyumna &
• Anirudha
Vasudeva
* Vasudeva – is Paramatma – the primary canvas
* He lives everywhere in all the Universes and in all the Hearts
* In Ramayana, Vasudeva is Rama and others are His brothers.
* In this material world, there is a Vaikunta Loka covered with water. This place is called Vedavati where Vasudeva lives.
Sankarshana
* Sankarshana – is Jivatma – integration/disintegration energy for material world
* Lord Sankarshana is the cause of 3 Purushas — Kaaranodakashayi, Garbodhakashayi and Kshirodhakashayi
Kaaranodakasayi – super soul (pervades) all collective universes
Garbodhakashayi – Pradhyumna – super soul of the collective living beings
Kshirodhakashayi – Anirudha – super soul of all individual living entities
* On top of Satya loka there is a Vishnuloka where Sankarashana lives, He is also at the bottom of the universe.
* From mouth of Sankarshana, the fire comes for partial destruction.
Pradhyumna
* Pradhyumna – is the intellect – resides in Dvaraka pura
Anirudha
* Anirudha – is the Ahamkara – controller of the mind – so pray to Lord Anirudha to make the mind turn towards the thoughts of Bhagavan.
* The Sun is the manifestation of Lord Anirudha.
* Sveta dwipa is on top of dhruva loka and Anirudha resides there. Brahma with other devas goes to Sveta dwipa and glorifies Anirudha.
* Sveta dwipa (also known as Ajitasya Padham) is a place situated in every universe (anda). It is a white island in the middle of ocean of milk.
* Anirudha is also the cause of Maha-Vishnu, from whose breathing the Rig Veda appeared.
* In the incarnation of Lord Krishna, Anirudha appeared as the son of the Lord. Lord Krishna in Dwaraka is the Vasudeva expansion of the original group.
S.B.1.5.37
Narada to Vyasadeva
नमो भगवते तुभ्यं वासुदेवाय धीमहि ।
प्रद्युम्नाय ऽनिरुद्धाय नमः सङ्कर्षणाय च ॥
Let us all chant the glories of Vasudeva along with His plenary expansions Pradhyumna, Anirudha and Sankarshana.
S.B.3.1.34
Vidhura to Udhava
अपिस्विदास्ते भगवान्सुखं वो
यः सात्वतां कामदुघो ऽनिरुद्धः ।
यमामनन्ति स्म ह शब्दयोनिं
मनोमयं सत्वतुरीयतत्वम् ॥ ३४॥
May I inquire whether Anirudha is doing well? He is the fulfiller of all the desires of the pure devotees and has been considered from yore to be the cause of the Ṛg Veda, the creator of the mind and the fourth plenary expansion of Vishnu.
S.B.3.26.28
श्रीभगवानुवाच to Devahuti
यद्विदुर्ह्य ऽनिरुद्धाख्यं हृषीकाणामधीश्वरम् ।
शारदेन्दीवर श्यामं संराध्यं योगिभिः शनैः ॥ २८
The mind of the living entity is known by the name of Lord Anirudha, the supreme ruler of the senses. He possesses a bluish-black form resembling a lotus flower growing in the autumn. He is found slowly by the yogis.
S.B.4.30.42
Prachetas Stuti
नमः समाय शुद्धाय पुरुषाय पराय च ।
वासुदेवाय सत्वाय तुभ्यं भगवते नमः ॥ ४२॥
Dear Lord, You have no enemies or friends. Therefore You are equal to everyone. You cannot be contaminated by sinful activities and Your transcendental form is always beyond the material creation. You are the Supreme Personality of Godhead because You remain everywhere within all existence. You are consequently known as Vasudeva. We offer You our respectful obeisances.
S.B.5.17.14
Sri Shuka to Parikchit
नवस्वपि वर्षेषु भगवान् नारायणो
महापुरुषः पुरुषाणां तदनुग्रहाय आत्म तत्व –
व्यूहेनात्मनाद्यापि सन्निधीयते ॥ १४॥
To show mercy to His devotees in each of these nine tracts of land, the Supreme Personality of Godhead known as Narayana expands Himself in His quadruple principles of Vasudeva, Sankarshana, Pradyumna and Anirudha. In this way He remains near His devotees to accept their service. Athma tatva vyuhena = By His four expansions
S.B.6.16.18 to 19
Narada to Chitraketu
ॐ नमस्तुभ्यं भगवते वासुदेवाय धीमहि ।
प्रद्युम्नाय ऽनिरुद्धाय नमः सङ्कर्षणाय च ॥
नमो विज्ञानमात्राय परमानन्दमूर्तये ।
आत्मारामाय शान्ताय निवृत्त द्वैत दृष्टये ॥
[Narada gave Citraketu the following mantra.] O Lord, O Supreme Personality of Godhead, who is addressed by the Omkara [praṇava], I offer my respectful obeisances unto You. O Lord Vasudeva, I meditate upon You. O Lord Pradyumna, Lord Anirudha and Lord Sankarṣhaṇa, I offer You my respectful obeisances. O reservoir of spiritual potency, O supreme bliss, I offer my respectful obeisances unto You, who are self-sufficient and most peaceful. O ultimate truth, one without a second, You are realized as Brahman, Paramatma and Bhagavan and are therefore the reservoir of all knowledge. I offer my respectful obeisances unto You.
S.B.10.16.45
Kaliya patni Stuti
नमः कृष्णाय रामाय वसुदेवसुताय च ।
प्रद्युम्नाय ऽनिरुद्धाय सात्वतां पतये नमः ॥
We offer our obeisances to Lord Kṛṣṇa and Lord Rama, the sons of Vasudeva, and to Lord Pradyumna and Lord Anirudha. We offer our respectful obeisances unto the master of all the saintly devotees of Vishnu.
S.B.10.40.21
Akrura Stuti
नमस्ते वासुदेवाय नमः सङ्कर्षणाय च ।
प्रद्युम्नाय ऽनिरुद्धाय सात्वतां पतये नमः ॥
Obeisances to You, Lord of the Satvatas (Yadavas), and to Your forms of Vasudeva, Sankarṣhaṇa, Pradyumna and Anirudha.
S.B.11.5.29
Karabhajana to King Nimi
नमस्ते वासुदेवाय नमः सङ्कर्षणाय च ।
प्रद्युम्नाय ऽनिरुद्धाय तुभ्यं भगवते नमः ॥
Obeisances to You, O Supreme Lord Vasudeva, and to Your forms of Sankarshana, Pradyumna and Anirudha. O Supreme Personality of Godhead, all obeisances unto You.
नारायण अखिल गुरो भगवन् नमस्ते ।
kNOw-me 