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Grasshopper's 3 Forces Of Social Interactions Force

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Grasshopper in a group are subject to attractive three forces based on combined sensory, chemical, and mechanical cues that affect their motion. These forcess represent the grasshopper swarming behavior and they are:
1. Downwind advection force
2. Social interactions force
3. Gravity force
There are N grasshoppers in the swarm group, and the ith grasshopper has position xi. The general grasshopper mathematical model is defined as follows: xi = Si + vg + va (1)
The direction of grasshopper swarm migration is strongly correlated with the direction of the wind and has little macroscopic motion in the transverse direction.
For simplicity, this mathematical model ignore the transverse direction, and hence the grasshopper mathematical model is two-dimensional

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