He is a leading expert in chaotic and complex dynamics, including fractal geometry and complex networks. His research involves bridging the gap between abstract concepts from mathematics and applications in the scientific and social disciplines, engineering, and medicine. He has made a huge impact in the area of control of chaos. The paper on this seminal work was selected by Physical Review Letters as a milestone in the past 50 years. He was awarded the Citation Laureate - Researcher of Nobel Class - in 2016, followed by a Motion to that effect supported by the Scottish Parliament. His scientific accomplishments include over 500 publications and over 450 invited talks. He received numerous distinctions, including multiple Doctor Honoris Causa and many Honorary Professorships, the Humboldt Senior Prize, Fulbright Fellowship, and Toshiba Chair as a World-renown Scholar. He is Fellow in various scientific societies, among them the Royal Society of Edinburgh, The World Academy of Sciences, the Academia Europaea, and the Brazilian Academy of Sciences. He has 26,000 citations and h-index = 76 in the Web of Science, and 41,000 citations and h-index = 92 in Google Scholar.