FPGA Realizations of Chaotic Epidemic and Disease Models Including Covid-19.

The spread of epidemics and diseases is known to exhibit chaotic dynamics; a fact confirmed by many developed mathematical models. However, to the best of our knowledge, no attempt to realize any of these chaotic models in analog or digital electronic form has been reported in the literature. In this work, we report on the efficient FPGA implementations of three different virus spreading models and one disease progress model. In particular, the Ebola, Influenza, and COVID-19 virus spreading models in addition to a Cancer disease progress model are first numerically analyzed for parameter sensitivity via bifurcation diagrams. Subsequently and despite the large number of parameters and large number of multiplication (or division) operations, these models are efficiently implemented on FPGA platforms using fixed-point architectures. Detailed FPGA design process, hardware architecture and timing analysis are provided for three of the studied models (Ebola, Influenza, and Cancer) on an Altera Cyclone IV EP4CE115F29C7 FPGA chip. All models are also implemented on a high performance Xilinx Artix-7 XC7A100TCSG324 FPGA for comparison of the needed hardware resources. Experimental results showing real-time control of the chaotic dynamics are presented.

Programmable constant phase element realization with crossbar arrays.

INTRODUCTION: Constant Phase Elements (CPEs) have been widely used in many applications due to the extra degree of freedom, which offers new responses and behaviors. OBJECTIVES: This paper proposes a new programmable CPE realization using resistive crossbar arrays. By programming the resistive devices, different CPEs can be obtained. METHODS: The proposed realization can be approximated as a weighted sum of low and high pass filters having the same cut-off frequency (i.e., Lapicque model). The closed-form approximation expression is derived, and then the Flower Pollination Algorithm (FPA) is used to find the optimal values of the network components. RESULTS: Different design examples are given over the frequency range of 106-109 rad/sec to prove the ability of this realization achieving any fractional order with less than 5% relative error in both phase and pseudo-capacitance. Monte-Carlo simulations are performed to evaluate the sensitivity of the proposed realization against device variability. In addition, multiple CPEs can be designed at the same time by utilizing the multiple ports of the crossbar array. The proposed realization is compared with two other state-of-art realizations showing comparable results as standalone realization and within fractional-order relaxation oscillator application. CONCLUSION: The proposed crossbar realization has proven its ability to realize any CPE with acceptable error. In addition, this multiple-port design offers high flexibility and on-the-fly switching of the CPE.

Monitoring of global cerebral ischemia using instantaneous phase variation plots.

In this paper, the derivative of the instantaneous phase of electroencephalographic (EEG) signals is used as a basis for monitoring of global cerebral ischemia. Visual and quantitative results were obtained from six rodents that were subject to 3, 5 and 7 minutes of global ischemic brain injury by asphyxic cardiac arrest. Results show that the variations in the instantaneous phase are capable of amplifying the variations during the various stages of the recovery process and may serve as a novel analytical approach to grade and classify brain rhythms during global ischemic brain injury and recovery.

Integrator-based circuit-independent chaotic oscillator structure.

An integrator-based chaotic oscillator structure composed of three cascaded inverting, noninverting, and differential integrators is presented. The nonlinearity responsible for folding the trajectories is introduced by a single switching diode which is controlled by the output of the first integrator in the cascade. Chaotic behavior is verified on the functional level of the structure rendering it circuit-independent. A possible circuit realization is given and a canonical single-parameter-controlled ordinary differential equation capturing the qualitative dynamics of similar fourth-order integrator-based chaotic oscillators is proposed.