Representation of Social Systems as Nonlinear, Complex, Self-Organizing and Closely Related to Biosystems and Mathematical Model of Their Evolution

On the basis of the systemic and synergistic approaches, the features and regularity of the selforganizing s ystems, i t i s c oncluded t hat t he s ocial s ystems a re nonl inear, open, c omplex, s elf-organizing systems. The scheme-model of the general structure of the social system is considered. Much attentions is given t o t he i nteractions of t he s ocial s ystems e lements w ith t he bi osystems. T he g raphic m odel-tree, reflecting the association between the social systems and the biosystems. In connection with that the most significant t echnologies a nd t he s cientific t rends, c onnecting w ith t he bi osystems: t he g ens, t he g enetic engineering, th e a rtificial in tellect, th e b ioand nanotechnologies, t he biomedicine, microbes, v iruses ar e considered. T he f utures of t he d ynamics o f t he s ocial s ystems a re not ed. I t i s s hown, t hat, w ith a hi gh probability, the spiral evolutionary p rocesses can occur in the social systems. The mathematical model i s presented, that describes the spiral structures, based on the Swift-Hohenberg equation.


Introduction
For the research, modelling, forecasting of the processes, occurring in the social systems, it is necessary to clearly represent, what t ype o f t he s ystems t he s ocial s ystems belong t o. T he s ystemic a nd s ynergistic ap proaches make it p ossible to believe th at social s ystems are nonlinear, open, complex, informational, self-organizing systems an d, t herefore, t hey h ave t he s ame features, regularity an d p roperties o f t he self-organizing s ystems [1 -9]. Based o n t he cu rrently av ailable i nformation about t he s ocial s ystems, o ne can classify them as t he self-organizing s ystems. T he s pecific p roperties o f th e social s ystems, ta king in to a ccount t he p eculiarities a nd regularity of the self-organizing systems, can be illustrated by the scheme shown in the Figs.1 and 2. Naturally, t he social s ystems can not b e co nsidered as isolated. I n r eality, th e social s ystems a re p art o f th e more co mplex s elf-organizing system.The relations a nd the i nteractions with t he t echnosphere, eco logyeconomic s ubsystems, t he ed ucational and cognitive spheres, t he d igital s phere an d t he b iosystems a re determined b y valuable information [ 9]. I n selforganizing systems the coherent processes occur due to the e xchange o f t he i nformation i n the form o f t he signals both between the parts of the subsystems and the structural le vels [ 4]. I nformation d etermines t he environment, i n which t he s ubsystems ar e l ocated an d the joint actions of which support it.  The i nformation d etermines t he o rder p arameters, that characterize the levels o f the system. As a result of the i nformation e xchange b oth t he system a nd t he subsystems ca n p ass from o ne s table state t o a n o ther, that, is, from one attraction to an other.
Nonlinearity m eans the m ultivariance of the system development p aths. T he s ocial s ystems ar e multi-levels. Macro l evel, o n t he o ne hand, i n many situations determines the behaviour and the structure of the parts of the system a t other l evels (meso, micro, na no), a nd o n the o ther hand, i ndividuals, gr oups, s ubgroups, subsystems can influence o n t he s ystem as a whole. Thus, the structure of a social system can be represented by the following general the scheme-model: Fig.3. The scheme-model of the social system structure.
In modern c onditions, t he s ociety has t o s olve complex problems in connection with t he necessary transition to a n ew le vel o f t he development, which i s determined b y the environment, t hat is , b y a ll components, t he d evelopment o f new t echnologies, t he managerial p roblems s olving, h umanity's e ntry i nto th e digital sphere, associated with artificial intelligence.
On t he o ne ha nd, a n i ndividual ( person) i s a s ingle element o f t he society. T hat i s a microparticle o f t he complex self-organizing macrosystem. T he place of the individual i n t he surrounding world. In the universe ha s been discussed for a long time in various directions. The individual (person) is by nature dualistic: it is necessary to distinguish between biological and social components. In the beginning, the biological evolution of man and the evolution o f t he s ocial r elations p roceeded i n p arallel. The p resent t ime is c haracterized by a slowdown in t he biological evolution a nd a n i ntensification o f t he evolution o f th e s ocial relations, t he c ollective intelligence o f h umanity an d an i ncrease i n t he r ole o f the s ocial v aluable i nformation. T he r ate o f t he development o f modern t echnologies, t he t echnosphere is a head o f t he s low d evelopment o f t he i ndividuals, psychics, the social institutions and the technology of the managerial de cisions a ssumption [ 10]. A pe rson i s connected t o t he society t hrough t he c ulture, economy, ecology, t echnology a nd r eligion. T he c omplication o f the te chnology le ads to th e complication o f t he s ocial relations. In such situation in order to conserve a p erson the society in the p rocess o f the s elf organization must develop new approaches, that allowed a p erson to orient in the changing reality, which is possible with the help of the science.

2
The graphical model-tree, demonstrating the social signifience of the biosystems  Microbes an d v iruses ca n b e concerned t o the nanobiosystems, which, as the experience and history of the development human s ociety have shown, a ffect society (epidemics, new diseases, the fight against which leads t o t he d evelopment of new t echnologies i n medicine). Mi crobes an d viruses are the self-organizing systems, and ha ve t he property of the self-defense, manifested i n t he f act t hat they mutate u nder t he influence o f the ma n-made p reparations to f ight t hem. This i s t he d anger to society on a g lobal scale from t he point of view of the nation health. In addition, microbes and viruses may b e used t o cr eate b acteriological weapons. Currently, the h istory o f t he c oronavirus demonstrates, h ow viruses c an e ffect o n p olitics, th e economy, the medicine, t he market, c ulture, ed ucation and the social-relations, medicine.
Genetic and the genetic engineering are the scientific direction, appeared at t he convergence of the sciences. By now, the nanotechnological results, achieved in these areas the significant and promising results for the future of the humanity: the study of genes and gens modifications, and DNA s tructure. T he manipulation with genes, with t heir s ubsequent i ntroduction i nto t he organisms cells make it possible to fight which incurable genetic diseases, to create new generations of drugs, to receive t he genetically modified p roducts, widely discussed in the s cientific world about, their usefulness and danger. The negative results o f t he noted above developments ar e the f ollowing: 1 ) th e development of various kinds of bi ological weapons, which a re a threat to all of the humanity; 2) works in some laboratories in the world t o cr eate ch imeras which a re unknown how they will end for society.
The biotechnologies [11] on t he o ne hand, also contribute to the development of the biological weapons types, a nd, o n t he o ther ha nd, s olve t he agricultural problems, develop alternative ways of obtaining energy, are used to co mbat environmental pollution, i n t he food industry. The cellular engineering, associated w ith the cultivation the cells a nd the tissues i n vitro, p lays a n important role in the study of the interactions of cells in the tissues, th e mechanisms of th e emergence a nd t he medical treatment o f the cancers, i n the breeding w ork and the creation of new drugs.
The bioelectronics allows the development of t he unique, hi gh-precision, control an d measuring methods in s cientific r esearch, m edicine and i ndustry. Biotechnology, in practice, straightens, the seemingly insurmountable d ifferences b etween p roduction, person, biomicrocosm a nd a llow c onsidering the following chain: biomicrocosm → person → society → production → nature.
In due time, the computer, information, technological revolutions were widely d iscussed. T he present t ime i s characterized b y t he co nvergence o f the sciences, technologies, digital revolution, which are actually based on the results of the previous revolutions. The formation of the digital sphere is associated with the developments in the field of the artificial intelligence the results of the brain s tructure studies, t he mechanisms o f the brain functioning, the achievements o f the neurophysiology, the mechanisms o f s elf-assembly o f t he molecular structures, information t ransfer in the biosystems, the automatic assembly of viruses, etc [10,14].
The digital sphere, digital technologies will open the digital world to the humanity and the individuals, change the relationships between the individuals and society. In this connection, it should be noted, that the digital technologies contain, dangers f or humans, since the society development ca n follow the path o f consciousness manipulating. The future will show, how the society, the economy, the politics and individual psychology will be transformed.
The biomedicine is a direction, which is successfully developing i n the health care an d p harmaceuticals. Mutating microbes and viruses pose ever more complex problems fo r the biotechnologists. T he de velopment of the intelligent b iomaterials i s o f g reat in terest in the biomedicine. Such materials are of the natural origin (for example, co llagen, k eratin) an d ar e u sed t o obtain implantable pr oducts, that ta ke in to a ccount i ndividual characteristics and are used in the surgery. With the help of s uch b iomaterials, i mportant p roblems of the interactions of cells with the surfaces of implants and the biological e nvironment are s olved, ensuring compatibility with b one, b lood, a nd a ntibacterial properties. By th is means th e intellectual materials help to improve the he alth of both the individual and society as a whole [12].
In t he field o f the nanotechnology, in i ncreasing frequency more a ttention is given to t he structures a nd the properties of the biosystem (molecular co mplexes, enzymes, D NA and RNA molecules and t he l ike), as a result, the d irection o f b ionanotechnology was f ormed [12 -15]. So, for example, the natural biosystems copies are r eproduced i n t he form o f the combinations of the sensors, detectors, indicators, act uators; the rotaxane molecules ar e used t o cr eate molecular memory. For creating the nanodevices, molecular s tructural b locks have b een d eveloped: b isaminoacids, from which bispeptides of a g iven s hape can b e constructed. I t is planned t o cr eate the nanodevices, capable o f the assembling, according t o a gi ven p rogram, nanomachines similar to the ribosomes, cap able o f synthesizing p rotein molecules from a mino a cids. T he combination of the bionanotechnology a nd a rtificial intelligence i s u sed t o cr eate of bi orobots, that have already been found the application in the socially useful activities.

Some development in research on social systems and the possible mathematical model of their evolution
Under t he i nternal o r the external i nfluences, the relations between the elements of the social systems can change while maintaining their main qualities. Under the influence o f s mall f luctuations, t he social system w ill adapt t o s uch ch anges and maintain t he s tructure as a whole. If structural changes exceed a certain threshold of "the sensitivity", the social system can go into a chaotic unstable state, when new internal relationships between elements are formed and the control parameters change. The d ynamic social s ystems in t heir d evelopment pass through the bifurcations points, at which t he changes in the stability and the transitions to the new e quilibrium states t ake p lace. I f a fter p assing t he b ifurcation p oint there is one variant of a stable state, then the evolution of the s ocial s ystem is p redictable, b ut if a multivariate situation develops, t hen t he evolution uncertainty appears.
In p ractice, in t he d ynamics of the multilevel nonlinear social systems, auto-oscillations c an form. Irreversible processes can be superimposed on the cyclic processes, an d the spiral e volutionary p rocesses are likely to arise [8]. The interaction between the elements of t he social s ystems and t heir i nteractions with th e systems as a whole is carried out through the information exchange. I n the social s ystems, the conditional a nd unconditional i nformations are generated. V aluable information i s of great i mportance for the evolutionary processes [9].
According to H. Haken [16], the public opinion plays the role o f t he o rder p arameter -the governing parameter which subjugates, the individuals, s preads throughout t he system, d eterming th e i nteraction between t he o rdered s tructure an d the individual elements of the system. Based on the above -mentioned it is possible to propose for discussion the mathematical model de scribing the spiral s tructures b ased o n t he Swift-Hohenberg equation: In the general case, t his e quation d escribes t he behavior of the system near the bifurcation p oints, the phase t ransitions, where β -is a p arameter, that determines the proximity of the system to the instability threshold, ε < 1 is a p arameter, depending o n t he environment p roperties. A special cas e o f t he equation (1) i n pol ar c oordinates for a homogeneous s olution u = 0 leads for the vector r = r(φ) to the equation of a logarithmic s piral, reflecting the e volution of the social system: where θ -the angle between the radius-vector of a point on the curve and the tangent to the curve at this point.

Conclusion
The s ystemic, s ynergistic a nd i nformational approaches u sed i n this p aper al low d rawing t he following conclusions: (1) the social systems are complex, open, multilevel, nonlinear, self-organizing systems that are in an equilibrium stable state with the coherent interactions of all t heir p arts d ue t o t he e xchanges o f t he i nformation signals flows; (2) fo r t he s elf-organization p rocesses t he conditional, unconditional and valuable information play both functional and controlling roles.
The transitions of the social systems from one state to another ca n o ccur under t he ex ternal a nd i nternal influences s uch a s o scilationss, which c an b e o f t wo types: (1) s mall o scilations that c hange t he s tructures a nd the behaviour of the subsystems but preserve the system as a whole; (2) o scillations e xceeding t he s ystem s ensitivity threshold and causing t he destruction o f the structure of the system as a whole. In this connection the dynamic of the s ocial s ystem d evelopment can b e r epresented as follows: with small fluctuations the system is capable of the s elf-healing, a nd when t he s ystem structure is destroyed, a chaotic state is formed, in which it gets to the b ifurcation p oint a nd r andomly c hooses a further development path (without external interferences).
In th is manner, t he p rediction o f the social s ystem behaviour is d ifficult, and when modeling the s elforganizing, c omplex s ocial s ystems, th e following factors s hould b e t aken i nto acco unt: ( 1) al l p rocesses occurring i n t he social systems ar e s elf-consisting probabilistic; (2) w hen m odeling s uch s ocial systems, it is practical to use a p robabilistic approach (for example, the mathematical formalism o f M arkov r andom processes), m odern th eories of o scillations a nd wa ves, game theory, theory of the decision making [5, 17 -20].
When studying and modeling all levels o f t he social systems, o ne s hould ta ke in to a ccount th eir c onnections with to biosystems. Currently, there is a global coronavirus a ttack a n a ll le vels o f the social systems. I t is cl ear t hat viruses an d ep idemics ca n b e used i n t he management o f t he s ocial systems. M any fields r elated to th e b iosystems ( genetics, b iotechnologies, bionanotechnologies, etc.) can influence the dynamics of the e ntire social systems , i ndividuals a nd c ontrol o f their evolution .