Chinese Journal of Physics 55 (2017) 692–697 Contents lists available at ScienceDirect Chinese Journal of Physics journal homepage: www.elsevier.com/locate/cjph Effects of agent’s orientation in 2D flocking models Redouane Bakir a,b , Iliass Tarras a,b,∗ , Laila Amallah a , Hicham Sbiaai a , Ahmed Hader a,d , M’Hammed Mazroui b , Yahia Boughaleb a,b,c a Laboratory of Biology, Geology and Enginery of Materials, Ecole Normale Supérieure, University Hassan II. Casablanca, Morocco b Laboratory of Physics of Condensed Matter, Faculty of sciences Ben M’sik, University Hasan II. Casablanca, Morocco c Laboratory of Physics of Condensed Matter, Faculty of sciences El- Jadida University Chouaib Doccali. El Jadida, Morocco d Regional Center for Education and Training, Settat, Morocco a r t i c l e i n f o Article history: Received 26 October 2016 Revised 9 April 2017 Accepted 10 April 2017 Available online 23 April 2017 Keywords: Flock Collective motion Noise Density Radius of repulsion Radius of orientation and Kinetic phase transition a b s t r a c t Various different types of collective motions have attracted attention from physicists; this is a fascinating phenomenon, resulting from the very simple interactions between individ- uals (particles/cells). Our aim is to contribute to elucidating the motion of collective behav- ior of a non-equilibrium multi-agent system. In this context, the topic of this manuscript is to study the effect of the zone of orientation on the collective motion in two-dimensional space. In this investigation, we extend the model suggested by Viscek et al. for only a sin- gle interaction radius. In our proposed model, the particles corresponding to agents locally interacting with their neighbors according to simple rules depending on the particular con- dition. At each time step the velocity of an agent depends on their direction and is per- turbed by an external noise η. Particularly, we show that with a specific fixed parameter a phase transition can be achieved, from disordered motion of particles to ordered mo- tion, by varying the radius of orientation R 2 and the value of the density. Furthermore, the value of R 2 at which the transition emerges depends strongly on the size of repulsion zone R 1 . The study is performed over different situations via a numerical simulation technique. Implications of these findings are discussed in the section of simulation results. © 2017 The Physical Society of the Republic of China (Taiwan). Published by Elsevier B.V. All rights reserved. 1. Introduction In nature, the collective motion of particles/cells is a fascinating phenomenon displayed by quite diverse types of indi- viduals at almost every spatial scale range in the natural world [1–3]. Self-propelled particle models play a crucial role in understanding the dynamics of complex systems. In reality, this behavior can be observed at almost every scale in nature from the macro scale where animals [4–7] prefer to move together in groups, such as bird flocks, herds of quadrupeds, human crowds, and fish schools, to microscopic scales such as single cells and unicellular organisms [8–10]. The charac- teristic of these groups is the onset of collective motion without a leader. During the last 15 years various methods and models have been suggested and tested to evaluate the main features of the collective motion of organisms [11–28]. How- ever, in spite of many efforts at understanding, the motion of complex systems has remained mysterious, due to the fact that the systems under study are not in equilibrium. The majority of biologists tend to describe collective behavior based on a description of each particular case. The approach used by physicists focuses on studying the statistical physics. In this context, the study of the complex motion of particles/cells was treated by Vicsek et al. in 1995 [1]. In their elegant model, ∗ Corresponding author at: Laboratory of Physics of Condensed Matter, Faculty of sciences Ben M’sik, University Hasan II. Casablanca, Morocco. E-mail address: iliass.tarra@gmail.com (I. Tarras). http://dx.doi.org/10.1016/j.cjph.2017.04.004 0577-9073/© 2017 The Physical Society of the Republic of China (Taiwan). Published by Elsevier B.V. All rights reserved.