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In the present study, we deal with the stability and the onset of Hopf bifurcation of two type delayed BAM neural networks (integer-order case and fractional-order case). By virtue of the characteristic equation of the integer-order delayed BAM neural networks and regarding time delay as critical parameter, a novel delay-independent condition ensuring the stability and the onset of Hopf bifurcation for the involved integer-order delayed BAM neural networks is built. Taking advantage of Laplace transform, stability theory and Hopf bifurcation knowledge of fractional-order differential equations, a novel delay-independent criterion to maintain the stability and the appearance of Hopf bifurcation for the addressed fractional-order BAM neural networks is established. The investigation indicates the important role of time delay in controlling the stability and Hopf bifurcation of the both type delayed BAM neural networks. By adjusting the value of time delay, we can effectively amplify the stability region and postpone the time of onset of Hopf bifurcation for the fractional-order BAM neural networks. Matlab simulation results are clearly presented to sustain the correctness of analytical results. The derived fruits of this study provide an important theoretical basis in regulating networks.

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Setting up differential models to give a description of the object economical phenomenon in the world today is very essential in economics and mathematics. In this current study, we are committed to the study on the anti‐control of Hopf bifurcation for a fractional‐order stable finance model. By virtue of a suitable washout filter controller involving time delay, we obtain a fractional‐order controlled finance model. Selecting the time delay as bifurcation parameter, we derive a new delay‐independent stability and bifurcation condition to assure that the involved fractional‐order controlled finance model is locally asymptotically stable and generates Hopf bifurcation around the equilibrium point. The investigation clearly manifests that the designed washout filter controller is a very effective means of bifurcation anti‐control. Ultimately, the obtained simulation figures and bifurcation diagrams are sufficiently presented to verify effectiveness for the proposed control technique. The established theoretical fruits have great significance in maintaining financial balance. Up to the present, the report on anti‐control technique of Hopf bifurcation for fractional‐order dynamical systems is quite rare. The research idea can also be applied to probe into the control issue of bifurcation and chaos for numerous other fractional‐order dynamical models in many areas.

Establishing financial models or economic models to describe economic phenomena in real life has become a heated discussion in society at present. From a mathematical point of view, the exploration on dynamics of financial models or economic models is a valuable work. In this study, we build a new delayed finance model and explore the dynamical behavior containing existence and uniqueness, boundedness of solution, Hopf bifurcation, and Hopf bifurcation control of the considered delayed finance model. By virtue of fixed point theorem, we prove the existence and uniqueness of the solution to the considered delayed finance model. Applying a suitable function, we obtain the boundedness of the solutions for the considered delayed finance model. Taking advantage of the stability criterion and bifurcation argument of delayed differential equation, we establish a delay-independent condition ensuring the stability and generation of Hopf bifurcation of the involved delayed finance model. Exploiting hybrid controller including state feedback and parameter perturbation, we efficaciously adjust the stability region and the time of occurrence of Hopf bifurcation of the involved delayed finance model. The study manifests that time delay is a fundamental parameter in controlling stability region and the time of onset of Hopf bifurcation of the involved delayed finance model. To examine the soundness of established key results, computer simulation figures are concretely displayed. The derived conclusions of this study are perfectly new and has momentous theoretical value in economical operation.