In this paper, we consider the n-term linear fractional-order differential equation with constant coefficients and obtain the solution of this kind of fractional differential equations by Adomian decomposition method. With the equivalent transmutation, we show that the solution by Adomian decomposition method is the same as the solution by the Green's function. Finally, we illustrate our result with some examples.

We establish the existence of traveling wave solutions and small amplitude traveling wave train solutions for a reaction-diffusion system based on a predator-prey model incorporating a prey refuge. By using the shooting argument, invariant manifold theory, and the Hopf bifurcation theorem, we analyze the dynamic behavior of this model in the three-dimensional phase space. Numerical results are also presented to illustrate the theoretical results.

Cooperative multi-agent reinforcement learning (cMARL) has many real applications, but the policy trained by existing cMARL algorithms is not robust enough when deployed. There exist also many methods about adversarial attacks on the RL system, which implies that the RL system can suffer from adversarial attacks, but most of them focused on single agent RL. In this paper, we propose a sparse adversarial attack on cMARL systems. We use (MA)RL with regularization to train the attack policy. Our experiments show that the policy trained by the current cMARL algorithm can obtain poor performance when only one or a few agents in the team (e.g., 1 of 8 or 5 of 25) were attacked at a few timesteps (e.g., attack 3 of total 40 timesteps).Preprint. Under review.

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