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Abstract: This paper considers a class of social foraging swarms with a nutrient profile (or an attractant/repellent) and an attraction–repulsion coupling function, which is chosen to guarantee collision avoidance between individuals. The paper also studies non-identical interaction ability or efficiency among different swarm individuals for different profiles. The swarm behavior is a result of a balance between inter-individual interplays as well as the interplays of the swarm individuals (agents) with their environment. It is proved that the individuals of a quasi-reciprocal swarm will aggregate and eventually form a cohesive cluster of finite size for different profiles. It is also shown that the swarm system is completely stable, that is, every solution converges to the set of equilibrium points of the system. Moreover, all the swarm individuals will converge to more favorable areas of the profile under certain conditions. For general non-reciprocal swarms, numerical simulations show that more complex self-organized rotation may occur in the swarms. [Copyright &y& Elsevier]

Abstract: In this paper, a three dimensional autonomous system which is similar to the Lorenz system is considered. By choosing an appropriate bifurcation parameter, we prove that a Hopf bifurcation occurs in this system when the bifurcation parameter exceeds a critical value. A formula for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions is presented by applying the normal form theory. Finally, an example is given and numerical simulations are performed to illustrate the obtained results. [Copyright &y& Elsevier]

Abstract: In this paper, the well known He’s variational iteration method (VIM) is used to construct solitary wave solutions for Boussinesq equation (BE). The chosen initial solution (trial function) can be in soliton form with some unknown parameters which can be determined in the solution procedure. [Copyright &y& Elsevier]