He has written solo, chamber, choral and orchestral music as well as electro acoustic music. Zivkovic achieved first particular recognition for his largely Violin Sonata (Metaphysical Poeme) from 1998 and Sad Songs (for soprano, viola and piano). Further performances lead to Fantasia for violin and wind orchestra which was premiered in 2001 at the Swedish Radio with Stockholm’s Wind Orchestra and B. Tommy Andersson as conductor, while Zivkovic played solo violin part.
Zivkovic collaboration with Trio Fibonacci, Canadian ensemble specially focused on contemporary music, has premiered his Piano Trio in Stockholm in 2002 at the Royal College Big Hall, and also recorded for Canadian Radio from the live concert in Montreal. He received notably success with his Serenade for strings performed by Musica Vitae in 2002/03 with leading of M.Bartosch, violinist and conductor. In 2005 he received the composition price at the First International Composers Competition pre-art in Switzerland for his piece Eclat de larme (The shine of the tear) for alto flute, oboe, accordion and piano. That piece was premiered in Zurich November 2005 and recorded for Swiss Radio. His piece The White Angel for chamber orchestra has been premiered with a great success at the Swedish Radio in March 2006 by SAMI Sinfonietta and K.Andreasson as a conductor. Among many of his works it should be mentioned also Sophisticated Preludes (for piano), Fantasmagoria for french horn and chamber orchestra, sextett Around the Candle Lights, Rhytmes, Cloches et Chansonne rituelle for percussion trio (performed by KMHs percussion trio) and Atmospheres Illuminees for violoncello and orchestra which still wait for its premiere.
Basically, the root of his compositions (and thoughts about music) lies in the inner psychical drama of the human being, the philosophy of the ancient Greeks, and, fundamentally, the artist’s questions about truth, man, destiny and tragedy (probably refers to Yugoslavian post-war syndrome). His music is very dense, often blurred with hundreds of details which are going against each other. He has developed his own theory about chords and scales which makes the base for most of his new works (the theory of harmonic system based on difference tones) allowing him mixture of tonal, atonal and microtonal world of sounds. He is influenced particularly by folklore (heterophony and polyrhythmic) as well as Octoechos (oktoiha) from the vocal music of the orthodox church which give his music its particularly colourful character. He is focused onto details coming out of these sources, interested in their microcosm and also in connections between sound and colour as natural phenomena (synesthesia). He received scholarship for composition from Swedish Development Agency (2000, 2001, 2002, 2003, 2004), and from Swedish Artists Association (2004, 2005, 2007), and also Royal Music Academy (2006, 2007). Zivkovic obtained as well his master degree in violin at the University of Music in Belgrade and further specialization at the Royal College of Music in Stockholm with K-O Mannberg. As a violinist, Zivkovic has performed at concerts in Sweden, Serbia, Montenegro, Croatia, Greece, Germany and Finland. He is an active player of contemporary music, and takes part as violin- and piano-improviser in a various groups for the contemporary music. He works as theory, harmony and composition teacher at Nordic Music Highschool in Stockholm.