Alternated Superior Chaotic Biogeography Based Algorithm for Optimization Problems

In this study, we consider a switching strategy that yields a stable desirable dynamic behaviour when it is applied alternatively between two undesirable dynamical systems. From the last few years, dynamical systems employed “chaos1 + chaos2 = order” and “order1 + order2 = chaos” (vice-versa) to control and anti control of chaotic situations. To find parameter values for these kind of alternating situations, comparison is being made between bifurcation diagrams of a map and its alternate version, which, on their own, means independent of one another, yield chaotic orbits. However, the parameter values yield a stable periodic orbit, when alternating strategy is employed upon them. It is interesting to note that we look for stabilization of chaotic trajectories in nonlinear dynamics, with the assumption that such chaotic behaviour is not desirable for a particular situation. The method described in this paper is based on the Parrondo’s paradox, where two losing games can be alternated, yielding a winning game, in a superior orbit.

Leveraging Parrondo's paradox for sustainable agriculture

Rotating crops is a sustainable agricultural technique that has been at the disposal of humanity since time immemorial. Switching between cover crops and cash crops allows the fields avoids overexploitation due to intensive farming. How often the respite is to be provided and what is the optimum cash cover rotation in terms of maximising yield schedule is a long-standing question tackled on multiple fronts by agricultural scientists, economists, biologists and computer scientists, to name a few. Dealing with the uncertainty in the field due to diseases, pests, droughts, floods, and impending effects of climate change, is important to consider when designing the cropping strategy. Analysing this time-tested technique of crop rotations with a new lens of Parrondo's paradox allows us to improve upon the technique and use it in synchronisation with the burning questions of contemporary times. By calculating optimum switching probabilities in a randomised cropping sequence, suggesting the optimum deterministic sequences and judicious use of fertilisers, we propose methods for improving crop yield and the eventual profit margins for farmers. Overall we also extend the domain of applicability of the seemingly unintuitive paradox by Parrondo, where two losing situations can be combined eventually into a winning scenario.

An alternating active-dormitive strategy enables disadvantaged prey to outcompete the perennially active prey through Parrondo’s paradox

Background Dormancy is widespread in nature, but while it can be an effective adaptive strategy in fluctuating environments, the dormant forms are costly due to the inability to breed and the relatively high energy consumption. We explore mathematical models of predator-prey systems, in order to assess whether dormancy can be an effective adaptive strategy to outcompete perennially active (PA) prey, even when both forms of the dormitive prey (active and dormant) are individually disadvantaged. Results We develop a dynamic population model by introducing an additional dormitive prey population to the existing predator-prey model which can be active (active form) and enter dormancy (dormant form). In this model, both forms of the dormitive prey are individually at a disadvantage compared to the PA prey and thus would go extinct due to their low growth rate, energy waste on the production of dormant prey, and the inability of the latter to grow autonomously. However, the dormitive prey can paradoxically outcompete the PA prey with superior traits and even cause its extinction by alternating between the two losing strategies. We observed higher fitness of the dormitive prey in rich environments because a large predator population in a rich environment cannot be supported by the prey without adopting an evasive strategy, that is, dormancy. In such environments, populations experience large-scale fluctuations, which can be survived by dormitive but not by PA prey. Conclusion We show that dormancy can be an effective adaptive strategy to outcompete superior prey, recapitulating the game-theoretic Parrondo’s paradox, where two losing strategies combine to achieve a winning outcome. We suggest that the species with the ability to switch between the active and dormant forms can dominate communities via competitive exclusion.

Parrondo's paradox for homoeomorphisms

We construct two planar homoeomorphisms $f$ and $g$ for which the origin is a globally asymptotically stable fixed point whereas for $f \circ g$ and $g \circ f$ the origin is a global repeller. Furthermore, the origin remains a global repeller for the iterated function system generated by $f$ and $g$ where each of the maps appears with a certain probability. This planar construction is also extended to any dimension $>$ 2 and proves for first time the appearance of the dynamical Parrondo's paradox in odd dimensions.

Parrondo’s Paradox for Tent Maps

In this paper, we study the dynamic Parrondo’s paradox for the well-known family of tent maps. We prove that this paradox is impossible when we consider piecewise linear maps with constant slope. In addition, we analyze the paradox “simple + simple = complex” when a tent map with constant slope and a piecewise linear homeomorphism with two different slopes are considered.

Fractals Parrondo’s Paradox in Alternated Superior Complex System

This work focuses on a kind of fractals Parrondo’s paradoxial phenomenon “deiconnected+diconnected=connected” in an alternated superior complex system zn+1=β(zn2+ci)+(1−β)zn,i=1,2. On the one hand, the connectivity variation in superior Julia sets is explored by analyzing the connectivity loci. On the other hand, we graphically investigate the position relation between superior Mandelbrot set and the Connectivity Loci, which results in the conclusion that two totally disconnected superior Julia sets can originate a new, connected, superior Julia set. Moreover, we present some graphical examples obtained by the use of the escape-time algorithm and the derived criteria.

The Dynamics of a Four-Step Feedback Procedure to Control Chaos

In this paper we make a description of the dynamics of a four-step procedure to control the dynamics of the logistic map. Some massive calculations are made for computing the topological entropy with prescribed accuracy. This provides us the parameter regions where the model has a complicated dynamical behavior. Our computations also show the dynamic Parrondo's paradox ``simple+simple=complex'', which should be taking into account to avoid undesirable dynamics.

Alternating lysis and lysogeny is a winning strategy in bacteriophages due to Parrondo’s Paradox

Temperate bacteriophages lyse or lysogenize the host cells depending on various parameters of infection, a key one being the host population density. However, the effect of different propensities of phages for lysis and lysogeny on phage fitness is an open problem. We explore a nonlinear dynamic evolution model of competition between two phages, one of which is disadvantaged in both the lytic and lysogenic phases. We show that the disadvantaged phage can win the competition by alternating between the lytic and lysogenic phases, each of which individually is a “loser”. This counter-intuitive result recapitulates Parrondo’s paradox in game theory, whereby individually losing strategies can combine to produce a winning outcome. The results suggest that evolution of phages optimizes the ratio between the lysis and lysogeny propensities rather than the phage reproduction rate in any individual phase. These findings are expected to broadly apply to the evolution of host-parasite interactions.