Theoretical and computational advances in nonlinear dynamical systems 2018

Peer reviewedPublisher PD

A Chaotic System with an Infinite Number of Equilibrium Points: Dynamics, Horseshoe, and Synchronization

Discovering systems with hidden attractors is a challenging topic which has received considerable interest of the scientific community recently. This work introduces a new chaotic system having hidden chaotic attractors with an infinite number of equilibrium points. We have studied dynamical properties of such special system via equilibrium analysis, bifurcation diagram, and maximal Lyapunov exponents. In order to confirm the system’s chaotic behavior, the findings of topological horseshoes for the system are presented. In addition, the possibility of synchronization of two new chaotic systems with infinite equilibria is investigated by using adaptive control

A new fuzzy reinforcement learning method for effective chemotherapy

A key challenge for drug dosing schedules is the ability to learn an optimal control policy even when there is a paucity of accurate information about the systems. Artificial intelligence has great potential for shaping a smart control policy for the dosage of drugs for any treatment. Motivated by this issue, in the present research paper a Caputo–Fabrizio fractional-order model of cancer chemotherapy treatment was elaborated and analyzed. A fix-point theorem and an iterative method were implemented to prove the existence and uniqueness of the solutions of the proposed model. Afterward, in order to control cancer through chemotherapy treatment, a fuzzy-reinforcement learning-based control method that uses the State-Action-Reward-State-Action (SARSA) algorithm was proposed. Finally, so as to assess the performance of the proposed control method, the simulations were conducted for young and elderly patients and for ten simulated patients with different parameters. Then, the results of the proposed control method were compared with Watkins’s Q-learning control method for cancer chemotherapy drug dosing. The results of the simulations demonstrate the superiority of the proposed control method in terms of mean squared error, mean variance of the error, and the mean squared of the control action—in other words, in terms of the eradication of tumor cells, keeping normal cells, and the amount of usage of the drug during chemotherapy treatment

Antimonotonicity, Crisis and Multiple Attractors in a Simple Memristive Circuit

Peer reviewedPostprin

Synchronization Phenomena in Coupled Birkhoff-Shaw Chaotic Systems Using Nonlinear Controllers

In this chapter, the well-known non-autonomous chaotic system, the Birkhoff-Shaw, which exhibits the structure of beaks and wings, typically observed in chaotic neuronal models, is used in a coupling scheme. The Birkhoff-Shaw system is a second-order non-autonomous dynamical system with rich dynamical behaviour, which has not been sufficiently studied. Furthermore, the master-slave (unidirectional) coupling scheme, which is used, is designed by using the nonlinear controllers to target synchronization states, such as complete synchronization and antisynchronization, with amplification or attenuation in chaotic oscillators. It is the first time that the specific method has been used in coupled non-autonomous chaotic systems. The stability of synchronization is ensured by using Lyapunov function stability theorem in the unidirectional mode of coupling. The simulation results from system’s numerical integration confirm the appearance of complete synchronization and antisynchronization phenomena depending on the signs of the parameters of the error functions. Electronic circuitry that models the coupling scheme is also reported to verify its feasibility