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Abstract In this manuscript, quaternion-valued delayed cellular neural networks are studied. Applying the continuation theorem of coincidence degree theory, inequality techniques and a Lyapunov function approach, a new sufficient condition that guarantees the existence and exponential stability of anti-periodic solutions for quaternion-valued delayed cellular neural networks is presented. The obtained results supplement some earlier publications that deal with the anti-periodic solutions of quaternion-valued neural networks with distributed delay or impulse or state-dependent delay or inertial term. Computer simulations are displayed to check the derived analytical results.

Abstract In this paper, we propose a new fractional-order financial model which is a generalized version of the financial model reported in the previous publications. By applying a suitable time-delayed feedback controller, we have control for the chaotic behavior of the fractional-order financial model. We investigate the stability and the existence of a Hopf bifurcation of the fractional-order financial model. A new sufficient condition that guarantees the stability and the existence of a Hopf bifurcation for a fractional-order delayed financial model is presented by regarding the delay as bifurcation parameter. The investigation shows that the delay and the fractional order have an important effect on the stability and Hopf bifurcation of involved model. Some simulations justifying the validity of the derived analytical results are given. The obtained results of this article are innovative and are of great significance in handling the financial issues.

Abstract We study the weighted pseudo almost periodic solutions of a Lasota–Wazewska system. With the aid of fixed point theory and differential inequality strategies, we give a set of new sufficient criteria that guarantee the existence and global exponential stability of weighted pseudo almost periodic solutions to a Lasota–Wazewska system. The obtained results of this manuscript are completely innovative and complement the work of Shao (Appl. Math. Lett. 43:90–95, 2015) to some degree. So far, no scholars have investigated this aspect.

Abstract We deal with Nicholson’s blowflies model with proportional delays. Employing the differential inequality theory, we give a new sufficient condition that guarantees the exponential convergence of all solutions of Nicholson’s blowflies model with proportional delays. Numerical simulations are put into effect to examine our theoretical findings. The derived results of this manuscript are innovative and complement some known investigations.

Abstract In this article, a kind of fuzzy cellular neural networks (FCNNs) with proportional delays and leakage delays are involved. Utilizing the differential inequality strategies, a sequence of sufficient criteria ensuring the global exponential convergence of involved model are presented. Computer simulations are performed to verify the analytic findings. The analytic findings of this article are innovative and complete several existing works.

This paper studies the global asymptotic stability for positive solutions to the higher order rational difference equation xn=(∏j=1m(xn−kj+1)+∏j=1m(xn−kj−1))/(∏j=1m(xn−kj+1)−∏j=1m(xn−kj−1)), n=0,1,2,…, where m is odd and x−km,x−km+1,…,x−1∈(0,∞). Our main result generalizes several others in the recent literature and confirms a conjecture by Berenhaut et al., 2007.