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Since the variable-order fractional systems show more complex characteristics and more degrees of freedom due to time-varying fractional derivatives, we introduce a variable-order fractional Hopfield-like neural network in this paper. First, the properties and dynamical behavior of the system are studied. The variable-order derivative’s effects on the system’s behavior are investigated through the Lyapunov exponents and bifurcation diagram; an emerging Feigenbaum tree of period-4 bubble is observed, which appears with the creation and annihilation of periodic orbits. A general basin of attraction for the fractional-order neural network is presented, demonstrating that its dynamical behaviors are extremely sensitive to initial conditions resulting in different periodic orbits and chaotic attractors’ coexistence. After that, an adaptive control scheme is proposed for the variable-order fractional system. Through Lyapunov …