When Lord Śiva was engaged in severely austere meditation, Cupid, the demigod of lust, threw his arrow of sex desire. Lord Śiva, thus being angry at him, glanced at Cupid in great wrath, and at once the body of Cupid was annihilated. Although Lord Śiva was so powerful, he was unable to get free from the effects of such wrath. But in the behavior of Lord Viṣṇu there is no incident of such wrath at any time.
(Srimad Bhagavatam----2:7:7----purport).

Originally Lord Rāmacandra is the incarnation of Vāsudeva, Lakṣmaṇa is the incarnation of Saṅkarṣaṇa, Bharata is the incarnation of Pradyumna, and Śatrughna is the incarnation of Aniruddha, expansions of the Personality of Godhead. Lakṣmījī Sītā is the internal potency of the Lord and is neither an ordinary woman nor the external potency incarnation of Durgā. Durgā is the external potency of the Lord, and she is associated with Lord Śiva.
(Srimad Bhagavatam----2:7:23----purport).

By the inconceivable energy of the Lord, every creative element has its own potencies, known as the potency of the element, potency of knowledge and potency of different actions and reactions. By a combination of such potential energies of the Lord there is the manifestation of creation, maintenance and annihilation in due course of time and by different agents like Brahmā, Viṣṇu and Maheśvara. Brahmā creates, Viṣṇu maintains, and Lord Śiva destroys. But all such agents and creative energies are emanations from the Lord, and as such there is nothing except the Lord, or the one supreme source of different diversities.
(Srimad Bhagavatam----2:9:28----purport).

This creation is very appropriately compared to clouds. Clouds are created or situated in the sky, and when they are displaced they remain in the same sky without manifestation. Similarly, the whole creation is made by the Supreme Personality of Godhead in His form of Brahmā, it is maintained by Him in the form of Viṣṇu, and it is destroyed by Him in the form of Rudra, or Śiva, all in due course.
(Srimad Bhagavatam----2:10:43----purport).

Lord Śiva tested Arjuna's strength by picking a quarrel with him over a hunted boar. He confronted Arjuna in the false dress of a hunter, and Arjuna covered him with arrows until Lord Śiva was satisfied with Arjuna's fighting. He offered Arjuna the Pāśupati weapon and blessed him. Here Vidura inquired about the great warrior's well-being.
(Srimad Bhagavatam----2:1:38----purport).

Lord Śrī Kṛṣṇa is so mild and merciful, as described in the above verses, and yet He is the Lord of all kinds of threes. He is the Supreme Lord of the three worlds, the three qualities of material nature and the three puruṣas (Kāraṇodakaśāyī, Garbhodakaśāyī and Kṣīrodakaśāyī Viṣṇu). There are innumerable universes, and in each and every universe there are different manifestations of Brahmā, Viṣṇu and Rudra.
(Srimad Bhagavatam----3:2:21----purport).

For the creation, maintenance and dissolution of the cosmic manifestations there are three incarnations: Brahmā, Viṣṇu and Maheśvara (Lord Śiva). They are the controllers or masters of the three modes of material nature, which cause the phenomenal manifestation. Viṣṇu is the master of the mode of goodness, Brahmā is the master of the mode of passion, and Maheśvara is the master of the mode of ignorance. There are different kinds of devotees according to the modes of nature. Persons in the mode of goodness worship Lord Viṣṇu, those in the mode of passion worship Lord Brahmā, and those in the mode of ignorance worship Lord Śiva. All three of these deities are incarnations of the Supreme Lord Kṛṣṇa because He is the original Supreme Personality of Godhead. The demigods directly refer to the lotus feet of the Supreme Lord and not to the different incarnations. The incarnation of Viṣṇu in the material world is, however, directly worshiped by the demigods. It is learned from various scriptures that the demigods approach Lord Viṣṇu in the ocean of milk and submit their grievances whenever there is some difficulty in the administration of universal affairs. Although they are incarnations of the Lord, Lord Brahmā and Lord Śiva worship Lord Viṣṇu, and thus they are also counted amongst the demigods and not as the Supreme Personality of Godhead. Persons who worship Lord Viṣṇu are called demigods, and persons who do not do so are called asuras, or demons. Viṣṇu always takes the part of the demigods, but Brahmā and Śiva sometimes take the side of the demons; it is not that they become one in interest with them, but sometimes they do something in order to gain control over the demons.
(Srimad Bhagavatam----3:5:43----purport).

The false ego of materialistic identity is controlled by the demigod Rudra, an incarnation of Lord Śiva. Rudra is the incarnation of the Supreme Lord who controls the mode of ignorance within material nature. The activities of the false ego are based on the objective of the body and mind. Most persons conducted by the false ego are controlled by LordŚiva. When one reaches a finer version of ignorance, he falsely thinks of himself as the Supreme Lord. That egoistic conviction of the conditioned soul is the last snare of the illusory energy which controls the entire material world.
(Srimad Bhagavatam----3:6:25----purport).

The tree of the material manifestation is described in the Fifteenth Chapter of Bhagavad-gītā as an aśvattha tree whose root is upward. We have actual experience of such a tree when we see the shadow of a tree on the bank of a reservoir of water. The reflection of the tree on the water appears to hang down from its upward roots. The tree of creation described here is only a shadow of the reality which is Parabrahman, Viṣṇu. In the internal potential manifestation of the Vaikuṇṭhalokas, the actual tree exists, and the tree reflected in the material nature is only the shadow of this actual tree. The impersonalists, theory that Brahman is void of all variegatedness is false because the shadow-tree described in Bhagavad-gītā cannot exist without being the reflection of a real tree. The real tree is situated in the eternal existence of spiritual nature, full of transcendental varieties, and Lord Viṣṇu is the root of that tree also. The root is the same—the Lord—both for the real tree and the false, but the false tree is only the perverted reflection of the real tree. The Lord, being the real tree, is here offered obeisances by Brahmā on his own behalf and also on behalf of Lord Śiva.
(Srimad Bhagavatam----3:9:16----purport).

The creation of Rudra from between the eyebrows of Brahmā as the result of his anger, generated from the mode of passion partly touched by ignorance, is very significant. In Bhagavad-gītā (3.37) the principle of Rudra is described. Krodha (anger) is the product of kāma (lust), which is the result of the mode of passion. When lust and hankering are unsatisfied, the element of krodha appears, which is the formidable enemy of the conditioned soul. This most sinful and inimical passion is represented as ahaṅkāra, or the false egocentric attitude of thinking oneself to be all in all. Such an egocentric attitude on the part of the conditioned soul, who is completely under the control of material nature, is described in Bhagavad-gītā as foolish. The egocentric attitude is a manifestation of the Rudra principle in the heart, wherein krodha (anger) is generated. This anger develops in the heart and is further manifested through various senses, like the eyes, hands and legs. When a man is angry he expresses such anger with red-hot eyes and sometimes makes a display of clenching his fists or kicking his legs. This exhibition of the Rudra principle is the proof of Rudra's presence in such places. When a man is angry he breathes very rapidly, and thus Rudra is represented in the air of life, or in the activities of breathing. When the sky is overcast with dense clouds and roars in anger, and when the wind blows very fiercely, the Rudra principle is manifested, and so also when the sea water is infuriated by the wind it appears in a gloomy feature of Rudra, which is very fearful to the common man. When fire is ablaze we can also experience the presence of Rudra, and when there is an inundation over the earth we can understand that this is also the representation of Rudra.
(Srimad Bhagavatam----3:12:11----purport).